How late? Which subway? Where?

If you're talking 10-11pm in Manhattan below 96th St (below 125th St on the 1 train) I'd say no problem.

If you're talking 3-4am in the South Bronx or East New York, a cab might be a good idea.

There are varying shades of gray in between.

The bad late-night subway experiences I've had (mostly in the 2-3am zone) have generally revolved around drunk teenagers puking on the train or having to wait forever due to service disruptions. I've taken the train late at night plenty of times and have never felt remotely threatened or seen anything resembling violent crime. I've twice seen dead people on trains or in the station, but both times were natural causes. It probably doesn't hurt, however, that I'm 6'1", male, don't dress fancy, don't use an iPod and don't wander the city drunk.

The only second-hand stories I've heard about people having trouble late at night revolve around drunk people passing out and waking up with their wallets (and/or shoes) missing.

I'd say ride the trains a couple times during the day. If you're comfortable with them then, you should be comfortable with them at night too, assuming you mind the others' advice here and stay alert, use common sense, etc. (which applies at all times in any city in the world).