My sink sprayer doesn't work. Is there some way to fix it without buying a new faucet and sprayer?:

Yes you can buy just the sprayer head or top at most big hardware stores, it unscrews at top, bring it with so the person helping you can get the right one for you.

Not really sure what you mean by it "doesn't work." One possibility might be the diverter inside the main faucet needs to be replaced. But, then again, it would help to have a little more information here.

Flyrod3wt - I would go with( clough's answer, )If the sprayer head is not plugged up , most of the time it IS the deverter, inside the actual faucet. Yes it can be replaced, ( THE DEVERTED). If you do it remember how you took it apart or get a plumber to do the job. Good luck.::: F.B.E.