The preposition "to" implies transfer and movement: something is changing location or ownership. "I give to others" means that something is changing ownership from me to other people. The preposition "for" talks about who receives a benefit; it doesn't necessarily tell us who or what receives the gift or object (in grammatical terms, we would say the "direct object"). As Charles said above, "I give for others" means that your gift giving benefits "others" somehow, but it doesn't necessarily mean that "others" directly receive the gift. Without more context showing that "others" are receiving the benefit of gift giving but not the gift itself, "to" is the better and more likely answer.

I think "give to" is correct. "Give for" means you are giving it in place of someone else -- they can't give it and you are giving it instead (for them).