The browser-based games I've played in recent times have been:
War of Empires *****: this remains, alongside Battlemaster, my favourite online game. Like BM, it is a bit of a one-man creation since it started some years ago, and that one man (Tom in BM, Bhaal in WoE) is frequently around to discuss things and explain things. It has a smaller playerbase than BM, so also has a everyone-knows-everyone community.
It has no roleplay at all, but the strategy and tactical options are fairly good, and one of the most impressive things is that you can do your battles and attacking when you're online - no "Your troops will arrive in 7 hours" stuff - which makes it immediate and more fun.
If you're the sort of player who likes the battles in battlemaster, but not the messages, and you find you have lots of extra time to play more games, you might like it.
Cantr II ****: played this for a fair while, and it's the most similar game to BM I've found. It's a similarly slow pace to battlemaster, is centred around roleplaying (more so than BM, really), and involves roleplaying normal people rather than nobles in a similarly kind of mock-medieval era. It's a bit slow to get going with, and the roleplay is all first-person stuff (ie you're talking to people in front of you, like a sort of roleplaying chatroom), so nothing like the third-person Roleplays we have in BM, or long narrative stuff, or even letters.
Tribal Wars **: Gah, that was a horrible game. The sort of game you can only do well in if you play all day and also in your sleep, and if you are willing and able to drop everything to make sure you send your troops at between 0 and 400 milliseconds after 14:05:34 in the afternoon (I'm not even exaggerating). Fabulous game if you live on your computer; horrible game if you are a human being. It seems involved at first, and then you realise it gets exponentially worse the longer you play.
Runescape ***: I guess that counts as a browser-based game since it's in a browser, but it's more like World of Warcraft, with massive playerbase and fancy graphics, and nothing like the others above which are more text-based and played mainly by adults. Runescape is dull as ditchwater most of the time, but has the one single benefit that you can pick it up and drop it again without any loss to your character. Going away for two weeks doesn't need you to pause anything, miss out on anything, lose anything etc. And in most cases you can drop it and log-out at a moment's notice with no bad consequences. It's also dull enough and repetitive enough that you can play it with only 10% of your brain turned on which is handy if you only needed 50% of your brain on that particular phonecall and wanted something else easy to stop you falling asleep.
It's one of the few I've found where you can very much fit it around your life, rather than having to fit your life around it, yet on the occasions you do have six hours in a row to fill, it can keep you completely occupied for the duration.
All the above are free and friendly and run on donations and love, with the exception of Runescape which is free to get about 15% of the game, but costs about USD$5 a month for the full game and is run by a faceless profit-making organisation.
