Actually, you can say "there you go" or "here you go" when giving something to someone. I think that "here you go" is much more often used in that situation.
Also keep in mind that "there you go!" can be said when someone is doing something or just did something well, as a form of encouragement. For example, if you were new at playing guitar and you were having trouble playing a note, and then after you tried for a while you did it correctly, I could tell you, "there you go! you're doing great!"