As perla said, they´re all pronouns, more specifically referring to the 2.person singular. However, they belong to different types of pronouns, namely subject pronouns, object pronouns and prepositional pronouns.
Tú - You (subject pronoun)
When the pronoun is the subject of a verb: You walk - Tú caminas; You speak english - Tú hablas inglés.
Te - You (object pronoun)
When the pronoun is the object of a verb: "I don´t see YOU" - "No TE veo".
This holds true for indirect objects as well as direct objects.
Ti - You (prepositional pronoun)
Prepositional pronouns is used after a preposition: This flower is for YOU - Esa flor es para TI
There are some exceptions to the rule of prepositional pronouns:
- "con": conmigo/contigo instead of "conmi"/conti"
- entre (between), excepto (except), incluso ("including" or "even"), menos ("except"), salvo ("except") and según ("according to") -- These all use the subject pronouns: "Yo" and "Tú" instead of "Mi" and "Ti".
Source: spanish.about.com