A locking tremolo allows you to do Dimebag-type squeals/dive bombs/horse noises etc, and the disadvantage is that if you have a bad one, it'll go out of tune.
A non locking tremolo will simply go out of tune when you use it. And you are much likelier to have a broken guitar neck prematuredly.
If you don't get a tremolo, you'll probably get a fixed bridge of some description. These tend to have better sustain, as well. You won't be able to do any whammy-tricks, though.
If you are not going to use one, its better not to get one, to be honest (particularly for double-locking types, which involve more complicated stringing and tuning... it does involve more work).