I've not played it personally, but I've heard some good stuff about Terra Est Quaestuosa (aka TEQ). It's browser-based, but as far as I can tell, it doesn't use Flash at all, it's completely browser-based. Might be worth a look...
TEQ Homepage
If you're looking for another way to kill a few minutes every day, you can always play Legends of Zork. The Activision crew has brought the realm of Zork into the browser-based world, and you can play with (and against) thousands of other players online. You get a limited number of turns per day, but it's been up long enough now that they've ironed out many of the bugs that plagued the launch version. No flash required, it just loads and plays in your browser.
Legends of Zork Homepage
And while I'm at it, I know you don't want a Flash-based game, but anybody interested in checking out a really cool visual novel that is totally and completely not safe for work (NSFW!), I encourage you to check out the Flash version of Divi-Dead as long as violence, nudity, and other things that you could see in any Rated R/18+ film don't upset you.
Divi-Dead Flash Version
Hope those help!
*huggles*
Areala