They all mean "and," but with differences in levels of formality. 与 is the most formal, and is used primarily in literary Chinese texts. 和 is the most "neutral" and the most common form of "and." 跟 is perhaps the most colloquial, and used in relaxed, informal speech. More so than the other forms, it also has a sense of "to follow" as well. So 我跟你去 not only means "You and I will go together," it also means "I will follow you there."

To tell you the truth the difference between them is very tiny. in spoken Chinese there is no need to differ.