Your primary goal with a zergling rush is to slow down or destroy your enemy's economy. The biggest mistake you can make is to forget that.
Did your opponent pull off all his workers and arrange them in a favorable formation to destroy your zerglings? Great! A worker that is in a standoff with your zerglings is mining just as effective as a dead worker.
That said, your zerglings are faster than enemy workers — if they've lined up to make a kill zone, then flank them. Pick off workers on the edges, don't just charge straight into the middle to get slaughtered.
Same with enemy defensive units. Isolated zealot pop out of the gateway? Kill it before it can meet up with the probes; rotate the zerglings to prevent deaths. Zealot in the minerals? Pick off the probes on the opposite side. All the probes clustered around the zealot in one corner of the minerals? Pick off the unprotected pylons.
In short, do not throw away zerglings — fight the battles you will win. If the opponent offers you a fight you'll lose, pick a different fight.