Few, when used without a preceding a, means "very few" or "none at all". On the other hand, a few is used to indicate "not a large number". The difference is subtle, yet there are instances where the two can mean completely opposite things.
I have a few objections to the vendor's proposed approach. implies that I am not on board with the vendor's proposal. I have some objections, but not so many as to say "I have several objections...". Nevertheless, I have objections that need to be addressed.
I have few objections to the vendor's proposed approach. is a more positive statement that implies I am more or less on board with the proposal. It is not a whole-hearted endorsement, but I barely have any objections at all.
edit Examples of Few and "A few"
- Few people in the history of the world were as evil as Hitler. means Hitler was among the most evil people in the history of the world. Hardly anyone was more evil.
- The supervisor was not inclined to approve the request without asking a few questions first.