well miniclip.com has changed now, and you can challenge other players, set up your account, have friends etc. have you tried there?

then there is runescape. but after you have done the quests, if you want to do more you will have to pay.
miniclip as above is a good site. there is a few games where you can interact with people, if you dont want to just play games by yourself.
There is Spineworld and i think its called the penquin game. those 2 games are interactive and no fees need to be paid.

You could try our very own Lycos games http://gameduell.lycos.co.uk/
My recommendation would also be puzzle pirates, very similar to runescape but more fun (imho) http://www.puzzlepirates.com/

Of course if you are not looking just for some mindless arcade game you could play on-line Scrabble against real opponents from all over the world at Internet Scrabble Club. There is a simple download to start off but I can vouch that it is virus-free. Here:
http://www.isc.ro/en/download.html
It's free , but there are some bells and whistles(extras) if you pay, I dont know what they are because the free version is a straightforward ordinary scrabble game and this is why I dont get in here very often these days.

i play www.darkorbit.com. gr€at gam€. chall€ngng from th€ start. a spac€ shoot€mup. fr€€, bt also has a paid v€rsion for b€tt€r ships/w€apons. brows€r bas€d. lots of qu€sts. chanc€ t win mon€y €v€n for th€ fr€€ v€rsion. if yu join, join my clan and i'll giv€ you af€w tips and cr€dits for a quick boost.