Obstruction is an automatic dead ball, but runners can be awarded whatever base the umpire thinks they would have gotten safely were it not for the obstruction.
If you tackled a runner, it would be a dead ball, but the umpire can just send the runner as far as he thinks he would have gotten on his own.
EDIT:
From the rule bueller posted:
If a play is being made on the obstructed runner, or if the batterrunner is obstructed before he touches first base, the ball is dead and all runners shall advance, without liability to be put out, to the bases they would have reached, in the umpire’s judgment, if there had been no obstruction. The obstructed runner shall be awarded at least one base beyond the base he had last legally touched before the obstruction. Any preceding runners, forced to advance by the award of bases as the penalty for obstruction, shall advance without liability to be put out.