I started using a laptop with gaming last year and find it a huge help. When running games I use a combination of the laptop and pencil/paper. The laptop is ideal for general reference (another vote for the Sovelior Sage SRD - awesome tool), displaying artwork and controlling music (huge collection of mp3s). I make sure to have the pdfs that I'll need open so that I can search nice and quickly (Google Desktop is also a big help). I use pen and paper for character stats (index cards - love 'em), initiative and combat and similar quick & dirty note-taking. When on vacation over Xmas, I happily ran a Rappan Athuk session with just the laptop and a battlemat (I also had the print version of the adventure on hand to save Alt-tabbing between screens when necessary).
When playing, I use the laptop exclusively and don't use pen or paper at all. I use notepad or Word to keep track of whatever I need to and make an editable pdf of my character sheet using form fields. I am basically a paperless player these days.
Downsides? Well, my initial motivation for incorporating a laptop was to cut down on the number of books that I carried to sessions. Instead, I carry a bag full of cables and laptop gear, so it's 6 of one and half a dozen of the other in that regard, lol.
Also, depending on the play area, sometimes I can't see the battlemat properly, and am always peering over the top of the screen. This is only a problem when I am a player, though. When DMing I make sure that I have enough room so that the laptop is off to one side and doesn't get in the way. As a player, though, I only have as much room as everyone else, so need to make do. Not a big problem when compared to the benefits.
I have also heard from one DM (in a passing comment, mind you, not as a serious gripe) that he didn't like players having laptops. Without wishing to be rude to anyone, I do fnd this attitude a tad petty. We can all see each others faces with no trouble, so I don't see the issue (other than the fact that the player has "hidden" his stuff from the DM - but if the DM doesn't trust the players, that's not actually a laptop issue imho). I haven't heard this raised as a serious problem, though.