It’s pretty much impossible for me not to say roll20.net. Roll20 has made gaming so much more accessible to so many people, but since we’re talking about my favourites here, I’ll just say that it’s helped me play games with a bunch more people I’d likely never have had the chance to game with otherwise. It’s a fantastic tool, well thought-out and well-designed. I’ve tried a number of remote/virtual-tabletop systems and all of them have been awful, with complex, esoteric interfaces that are completely non-obvious or helpful. Roll20 just works and is pretty much obvious – at least for doing the basics. Sure, it might not have super complex, deep rules knowledge and simulation abilities – but equally it doesn’t take forever to setup, especially when you aren’t running some pre-published pay-for module for it.
I can’t recommend roll20 enough and I’ve used it for man types of games, including Fiasco, Numenera, Pathfinder and others.
The other website that comes in close second is RPoL. RPoL is a play-by-forum website that has a bunch of tools for managing complex games with larger numbers of players. It’s not the prettiest website, but I’ve tried a number of different sites and something about RPoL just keeps me coming back. Its ugly simplicity is its strength, because it’s just easy to do things, even though sometimes it is not immediately obvious. No bullshit complex UIs, just dumb, simple forms for everything. It’s got all the tools I need from a play-by-forum site and while literally every game I’ve ever played there has fallen apart, it’s still the bar against which I measure all other play-by-forum websites.