Carcasonne : very easy to adapt for kids. Only takes about an hour; involves building and claiming cities, roads, missions and farms - no war themes.
Ticket to Ride: again very kid (and not-interested-in-gaming family friendly). Involves collecting card "engines" to build most effecient train yo random destinations. Maybe takes 90 minutes tops.
EuroRails/RussiaRails: more complex than Ticket to Ride ; involves choosing wisest touted to collect and deliver resources. Not aggressively competitive (you mostly just do YOUR best and don't block others. Takes a few hours.
Killer Bunnies : fun but can be competitive and cutthroat (which led to a wildly entertaining and infamous screaming showdown between a few ADULT relatives a few years ago.
Seven Wonders: this is my new fav...involves collecting and buying appropriate resources, buildings, etc based on you "wonder" society. Goes quickly - 30 minutes maybe?
Settlers of Catan: got a day to waste? Build your most resourceful settlements while blocking out others.
A great list. I'd add Agricola and Pandemic, as more recent games that are a lot of fun. (Agricola is themed around a family struggling to feed themselves and build a farm; Pandemic is a group of CDC workers battling disease around the world.) Pandemic (and its little sister Forbidden Island) is particularly nice because it's a cooperative game - everyone working together to beat the game - so it doesn't invite as many losing-related disputes. Dominion is also great - it plays a little bit like MtG, as I understand it, but everyone starts with the same deck and range of cards that can be added to it (a different set every time).
Lots of replay value, even with the base set, and there are now seven expansions, with one more small one planned.
