Even avoiding REGISTERING for the draft can get you in legal trouble, let ago dodging it if you actually are drafted. This is for people who avoid registering:

[qq]The government may prosecute a potential draftee who does not register with the SSS. If convicted, the man would face up to five years in jail and a fine of up to $250,000. Today, the government is unlikely to take such extreme action. Instead, it encourages registration by withholding government benefits from potential draftees in violation. This includes federal financial aid for school, federal job training and some federal employment. Additionally, all eligible aliens must register before gaining U.S. citizenship. The SSS reports that in 2000, 88 percent of eligible men were registered.[/qq]

Also, if you're a "conscientious objector", you still get drafted, you just get assigned to a non-combat duty.