The only one button skill-based one
Metro Siberia kicks some skill into our showcase with its simple but beautifully challenging sci-fi tinged pilot action schtick. It combines the appeal of all-in-the-timing games like Whack the Penguin with the old school stylings of Asteroids, requires just a single button, and produces more heart-in-mouth moments than a cannibal feast. Enjoy it at RockPaperShotgun.
The village-building, troop-training one
Travian is a huge resource-management game whose potentially intimidating scope and complexity is camoflauged nicely behind pretty pictures and super-easy menus. There's a huge number of this type of browser games, but Travian is by far the nicest to play.
First, you'll sign up to a server full of other players and start managing your own little village. By juggling how much wood to cut, clay to gather, crops to harvest or iron to mine, you'll build out into a bigger and bigger settlement. The players surrounding you can be traded or allied with. Or they might just decide to raid your hard-earned resources. Damn them.
What's great about Travian, and all the best browser games, is that it never gives you quite enough. You'll manage to build maybe two or three buildings, troops or resource areas per day, if that, which gives Travian a slow but satisfying pace, while treating you just mean enough to keep you keen as ever to return.