I quit my job with no notice. Can they withhold the vacation hours accumulated?

I agree with the previous answer in general, however, even if you are owed vacation pay, the fact that you quit with no notice could give your employer a counterclaim or setoff if they can show that the lack of notice caused them some harm or damage, such as the extra expense of a temporary person to fill in for the typical two week notice period or overtime paid to other employees to fill in for you during the two week period. 

Depends entirely on (1) your contract, if you had one; and (2) the company's policies, as set out in writing (e.g. an employee handbook) or at least as demonstrated by how they've treated other people. If there's anything in writing, that will control; if not, what has happened when other people quit? Even if no one quit w/o notice, what happened when people left for other jobs? There is no general law about vacation days, it is up to the company to set its policy--but then it has to at least treat it's employees the same under the policy.