Check out his filmography. Dude took a huge plunge in the 90s. The drug thing hit his career hard. Plus I think he was a huge liability for any movie.

I remember it being a pretty slow comeback. The first 'could he be back?' buzz that I remember was Two Girls and A Guy (I'm pretty sure nobody went to see U.S. Marshalls because of him). It was a slow creep up from there, with Ally McBeal, Kiss Kiss Bang Bang, even The Singing Detective.

But for the mainstream it wasn't a proper comeback until Iron Man. And I'd say nowadays, more people know him from that than from anything he did in the 80s.

However I don't think that's so for Jude Law. His breakout performance was Gattaca (I don't know if him being in a wheelchair the whole time can be considered coasting on sex appeal). And then he hit it big with Talented Mr Ripley, the Oscar nod role. It seems like he's been an A actor since then. Outside of a few romantic comedies, I wouldn't say he's coasting on his looks, but that's just my opinion.