I've always been big on digital tabletop gaming; when I host games it looks like a LAN party with a ton of laptops for my players and I to use. I've found it incredibly liberating to handle all of my would-be physical functions on the computer, mostly due to expense. After all, it costs nothing to get a die roller (my personal favorite browser-based one being at donjon.bin.sh, though I often use ones integrated into various game-specific character creators because they're already open), while a full set of polyhedral dice can cost a chunk depending on when you're getting them.
In addition, I use a digital tabletop because it allows me to be lazy as a GM. Previously I've been using stuff like MapTool to place down objects, but when I'm really in a time crunch I've been known to be lazy and just pull up Inkscape and doodle out stuff, then connect my laptop to a display everyone can see. I'm excited about the upcoming Roll20 which looks like it could revolutionize the way digital tabletops work, especially since it includes a real-time object search that would make my frantic Inkscape doodles obsolete.
But the better question is why?
The digital tabletop is capable of running a lot of stuff at once; what would have previously been several sheets of paper can be reduced into a file or two relatively easily. I use all my books in PDF format, especially since I can't stand bending up my books, but also because of features such as being able to search through the whole text in order to finish stuff off. I'm also a big fan of the PDF for character sheets, though I'm not ashamed to use a more complex system-specific character management tool like Chummer in order to have a one-stop shopping place. In addition, I can set up Chummer to handle my own house-rules for NPC creation when I want to keep track of the general power level of opponents and allies, and then tell my players how I want them to set it up so that they can compete. It makes gaming a lot more liberating as well, since my players don't have to know about the full character creation process in order to understand what's going on. I have some players who try to use the character generators without even consulting the rulebooks or myself, and that ends pretty poorly, but usually I've found that having a character management tool frees up my players to do what they need to do rather than worry about bookkeeping; Chummer's a particularly nice one but even something as simple as a customized spreadsheet with a lot of calculations does the trick for some games.
On an unrelated note, this is why I like to put out interactive PDF character sheets for my games, because I like to provide a useful tool for fellow Game Masters and just to generally help players along.
In addition to this, the digital tabletop means that distance is often a non-issue. While I've always had connectivity issues with certain players, I've found that I am often able to work in a player who lives nine hours away from the rest of the group without too many issues, though I'm looking forward to seeing if Roll20's voice chat integration works better than, say, Infrno's, which worked fine for me but tended to fail for my players. As a general rule, I can have one player connect from a remote location, meaning that I almost never have to worry about catching up the occasional absentee. In addition, should I ever have a situation where there's enough players to play but still a couple missing, sitting at a laptop means that I can just turn on my microphone and record the audio in order to save a record for later, which I can then send to my missing players.
Another thing I find useful about an all-digital approach is that it allows me to have a session with very little gear; where I would previously need to bring dice, books, and potentially even other gear, I can get by with just my laptop and not need to bother with carrying books, which means I can get going quickly and don't have to worry too much about forgetting stuff, since it's much easier to keep track of one thing than many when moving from place to place. It also means that I have access to a variety of additional enhancements such as audio tracks and the like because I've already got my laptop handy.
Of course, there are downsides; I've noticed that my players are frequently focused on Facebook or even on occasion video games during the middle of a session, and there's always the temptation for me to do the same. You miss something when you've got the laptop in front of you as well, you don't get the same depth you get with traditional pen and paper gaming, since you don't see each others' faces as much. In addition, I've found that dealing with tech can take a chunk out of session time: Mashupforge lets you have great maps with location indicators, but if the temptation comes to add every location the players have ever visited and you start wasting a couple minutes to set up each location you'll wind up hurting the play experience.
Those are my two cents, post your thoughts below.