Saraswati Puja
This time of year we pray to Saraswati Devi and Lord Hayagriva to bless us with wisdom and knowledge. Aside from the festive aspects of Navaratri, such as assembling various dolls and figures and constructing elaborate facades for the Navaratri golu and inviting sumangalis over, we primarily celebrate the active presence of Lakshmi Thaayaar during this festival, culminating with the honoring of Her in the form of Saraswati Devi, the Goddess of all learning and speech.

Sri Sadagopan has written quite elaborately about the Vedic concept of Saraswati in previous years:

According to the understanding of some acharyas, as the presiding deity of all speech, Saraswati is appropriately the consort of Lord Hayagriva, and is not to be confused with the later Puranic notion of a Saraswati being the wife of Brahma  (sarojAsana-dharma-patnI). Accordingly, She is Lakshmi Herself; if Hayagriva represents the essence of the Vedas, She is the sound of this essence, related inseparably to it.

uväca puratas tasmai
tasya divya sarasvaté
käma-kåñëäya govinda
he gopé-jana ity api
vallabhäya priyä vahner
mantram te däsyati priyam
uväca—said; purataù—in front; tasmai—to him; tasya—of Him (the Supreme Lord); divyä—divine; sarasvaté—the goddess of learning; käma—the käma-béja (kléà); kåñëäya—to Kåñëa; govinda—govindäya, to Govinda; he—O; gopé-jana—of the gopés; iti—thus; api—also; vallabhäya—to the dear one; priyä vahneù—the wife of Agni, Svähä (the word svähä is uttered while offering oblations); mantram—mantra; te—to you; däsyati—will give; priyam—the heart’s desire.
Then the goddess of learning Sarasvaté, the divine consort of the Supreme Lord, said thus to Brahmä who saw nothing but gloom in all directions, “O Brahmä, this mantra, viz., kléà kåñëäya govindäya gopé-jana-vallabhäya svähä, will assuredly fulfill your heart’s desire.” (Brahma Samhitaa. 5:24.)

Some take the following paasuram from Tirumazhisai Alvar's Naanmukan Thiruvantaati to be a reference to this aspect of Lakshmi-Saraswati:

  veRpenRu vEngadam paadinEn, vIdaakki
  niRkinREn ninRu ninaikkinREn, - kaRkinRa
  noolvalaiyil pattirundha noolaatti kELvanaar,
  kaalvalaiyil pattirundhEn kaaN. (40)
Here "noolaatti", the lady of the books, is taken to be a reference to the Goddess. (Alternatively, it also means the lady spoken of by the books, i.e., Vedas). Since noolaatti kELvanaar is identified with the Lord of Venkatam, Saraswati is none other than a form of Lakshmi.

On the ninth day of Navaratri, known as Mahanavami, there is also what is known is "Ayudha pUja". I don't know if it is universally celebrated -- members are requested to clarify -- but on this day, all animals, equipment, etc.,used in one's profession are ceremonially prayed for and blessed.

Vishnu Purana upholds:

      tvam siddhis tvam svadha svaha
       sudha tvam loka pavani
      sandhya ratrih prabha bhutir
       medha sraddha saraswati
"You are siddhi, nectar, Svaha and Svadha, O purifier of the worlds. You are twilight, night, effulgence, opulence, intelligence, faith, and Saraswati." (Sri Laxmi Stuti Visnu Purana, VII.9.119.)
 kåpä-päräväraù sajala-jalada-çreëi-ruciro
 ramä-väëé-rämaù sphurad-amala-paìkeruha-mukhaù
surendrair ärädhyaù çruti-gaëa-çikhä-géta-carito
 jagannäthaù svämé nayana-patha-gämé bhavatu me
Lord Jagannätha is an ocean of mercy and He is beautiful like a row of blackish rain clouds. He is the storehouse of bliss for Lakñmé and Sarasvaté, and His face is like a spotless full-blown lotus. He is worshiped by the best of demigods and sages, and His glories are sung by the Upaniñads. May that Jagannätha Svämé be the object of my vision." (Jagannath Ashtakam 4.)
jéyät kaiçora-caitanyo
mürti-matyä gåhäçramät
lakñmyärcito ’tha väg-devyä
diçäà jayi-jaya-cchalät
Long live Lord Caitanya Mahäprabhu in His kaiçora age! Both the goddess of fortune and the goddess of learning worship Him. The goddess of learning, Sarasvaté, worshiped Him in His victory over the scholar who had conquered all the world, and the goddess of fortune, Lakñmédevé, worshiped Him at home. Since He is therefore the husband or Lord of both goddesses, I offer my obeisances unto Him. (Sri Chaitanya Charitamrta. Adi lila 16:3.)
kämais tais tair håta jïänäù
prapadyante ’nya-devatäù
taà taà niyamam ästhäya
prakåtyä niyatäù svayä
“Those whose minds are distorted by material desires surrender unto demigods and follow the particular rules and regulations of worship according to their own natures.” (Bg. 7.20)
There are many different types of men in the world, and they’re functioning under the different modes of material nature. Generally speaking, most men are not after liberation. If they take to spirituality, they wish to gain something by spiritual power. It is not uncommon in India for a person to go to a svämé and say, “Swäméji, could you give me some medicine? I am suffering from this disease.” He thinks that because a doctor is too expensive, he can go to a svämé who can work miracles. In India also there are svämés who go to people’s houses and preach, “If you give me one ounce of gold I can make it into one hundred ounces of gold.” The people think, “I have five ounces of gold. Let me give it to him, and I’ll get five hundred ounces.” In this way the svämé collects all the gold in the village, and after collecting it, he vanishes. This is our disease: when we go to a svämé, or a temple or a church, our hearts are filled with material desires. Wanting some material profit out of spiritual life, we practice yoga just to keep our health fit. But, in order to keep healthy, why take shelter of yoga? We can become healthy through regular exercises and regulated diet. Why resort to yoga? Because: kämais tais tair håta-jïänäù. We have the material desire to keep ourselves fit and to enjoy life by going to church and making God our order-supplier.
Having material desires, men worship various demigods. They have no idea how to get out of matter; they want to utilize the material world to its best capacity. For instance, in Vedic literature there are so many recommendations: if one wants to cure his disease, he worships the sun, or if a girl wants a good husband, she worships Lord Çiva, or if one wants to become beautiful, he worships such and such god, or if one wants to become educated, he worships goddess Sarasvaté. In this way Westerners often think that the Hindus are polytheistic, but actually this worship is not to God, but to demigods. We should not think that the demigods are God. God is one, but there are demigods who are also living entities just like us. The difference is that they have a considerable amount of power. On this earth there may be a king or a president or a dictator—these are men like us, but they have some extraordinary power, and in order to get favors from them, to take advantage of their power, we worship them in one way or another. But Bhagavad-gétä condemns worship of the demigods. This verse clearly states that people worship the demigods due to käma, material lust.
This material life is simply based on lust; we want to enjoy this world, and we love this material world because we want to gratify our senses. This lust is a perverted reflection of our love of God. In our original constitution we are made to love God, but because we have forgotten God, we love matter. Love is there. Either we love matter, or we love God. But in no case can we get out of this loving propensity; indeed, we often see that when one doesn’t have children, he loves a cat or a dog. Why? Because we want and need to love something. In the absence of reality, we put our faith and love in cats and dogs. Love is always there, but it is distorted into the form of lust. When this lust is baffled, we become angry; when we become angry, we become illusioned; and when we are illusioned, we are doomed. This is the process that is going on, but we have to reverse this process and turn lust into love. If we love God, we love everything. But if we do not love God, it is not possible to love anything. We may think that it is love, but it is simply a glamorized form of lust. Those who have become the dogs of lust are said to have lost all good sense: kämais tais tair håta-jïänäù.
There are many rules and regulations for the worship of demigods in the scriptures, and one may question why the Vedic literatures recommended their worship. There is necessity. Those who are motivated by lust want the opportunity to love something, and the demigods are acknowledged as the officers of the Supreme Lord. The idea is that as one worships these demigods, he will gradually develop Kåñëa consciousness. But if one is completely atheistic and disobedient and rebellious against any authority, what hope is there? So one’s obedience to a higher personality can start with the demigods.
If, however, we take directly to the worship of the Supreme Lord, worship of the demigods is not necessary. Those who worship the Supreme Lord directly show all respect to the demigods, but they do not need to worship them because they know that the supreme authority behind the demigods is the Supreme personality of Godhead, and they are engaged in worshiping Him. In any case, respect is still there. A devotee of the Lord shows respect even to an ant, what to speak of the demigods? The devotee is aware that all living entities are parts and parcels of the Supreme Lord and that they are playing different roles only.
In relation to the Supreme Lord, all beings are to be respected. Therefore a devotee refers to others as “prabhu,” meaning “My dear sir, my dear lord.” Submissiveness is a qualification for a devotee of the Lord. Devotees are kind and obedient, and they have all good qualifications. In conclusion, if one becomes a devotee of the Lord, all good qualifications will automatically develop. By nature, the living entity is perfect, but due to the contamination of lust, he becomes vicious. That which is part and parcel of gold is also gold, and whatever is part and parcel of the Complete perfect is also perfect.
                                                oà pürëam adaù pürëam idaà
                                                pürëät pürëam udacyate
                                                pürëasya pürëam ädäya
                                                pürëam evävaçiñyate

“The personality of Godhead is perfect and complete. Because He is completely perfect, all emanations from Him, such as this phenomenal world, are perfectly equipped as a complete whole. Whatever is produced of the complete whole is also complete in itself. Because He is the complete whole, even though so many complete units emanate from Him, He remains the complete balance.” (Çré Éçopaniñad, Invocation)
    Due to the contamination of matter, the perfect living entity falls down, but this process of Kåñëa consciousness will again make him perfect. Through it, he can become truly happy, and after leaving the material body, enter into the kingdom where there is eternal life, bliss and full knowledge. (A.C. Bhaktivedanta Swami Prabhupada. Book - On the way to Krishna. Chapter 5.)

"Çréla Bhaktisiddhänta Sarasvaté Gosvämé Mahäräja has remarked that there is a class of common men who claim that anyone and everyone can worship the Supreme Lord according to his own invented mode of worship and still attain the Supreme Personality of Godhead. They claim that one can approach the Supreme Lord either through fruitive activities, speculative knowledge, meditation or austerity and that any one of the methods will succeed. They claim that one can accept many different paths and still reach the same place, and they maintain that the Supreme Absolute Truth may be worshiped either as the Goddess Kälé, or Goddess Durgä, or Lord Çiva, Gaëeça, Räma, Hari, or Brahmä. In short, they maintain that it does not matter how the Absolute Truth is addressed, for ali names are one and the same. They give the example of a man with many names; if he is called by any of those names, he will answer.
Such views may be very pleasing to an ordinary person, but they are full of misconceptions. One who worships the demigods, motivated by material lust, cannot attain the Supreme Personality of Godhead. If one worships the demigods, the external energy of the Lord can award some results, but this is not to say that one can attain the Supreme Lord by such worship. Indeed, their worship is discouraged in Bhagavad-gétä: 7:23." (A.C. Bhaktivedanta Swami Prabhupada. TLC. Chapter 29.)