I've taken the morning after pill a couple of times and not had any side effects, although I know some of my friends said they felt rough afterwards.
I've never had to take it myself, but my old roommate did - cramps of doom, headaches, some nausea. Not, like, world-ending crap, but generally feeling super run-down and 'staying on the couch with TV and advil and a hot water bottle, come get me in 2 days'. Not something I'd voluntarily sign up for.
Not to derail, but...I've heard things like this before (usually regular period related), and always wondered: what exactly do you DO with the hot water bottle??
Fill it with super-hot water and put it on your stomach - like, lower stomach, just above the pubic bone. It helps with cramps A LOT (usually more than advil or aleve).
Bad cramps, for the men here, basically feel like having an iron railroad spike dug into the bit of skin between the hipbone and stomach (like, where the ovaries are, if you look at a diagram...) right through your stomach and into the lower back. Basically, if it's really bad, you wind up curled up around the pain in a fetal position. Advil takes a half-hour to kick in, so you take the advil (because effing OW), but the hot water bottle is a muscle relaxant that really helps the pain immediately... but once the heat goes away, the pain comes back.
Hot baths help, too - same logic.