Tom
At my UK Clubs (Aberdour and Dornoch) foresomes are rarely played except in competition. That being said, there are so many competitions available, both intraclub and Open, I get to play foursomes from 5-20 times per year, both match play and stroke play. One of the staples of the UK competitive circuit is the interesting concept of "mixed" foursomes which pits couples against couples, usually in 18-hole stroke play events, but most famously in the week-long match play torunament at Worplesdon. Worplesdon interestingly includes both man and lady professionals along with the amateurs. Playing a mixed foursomes with your partner is a very good way to assess the stability of your relationship. Intraclub foursomes tends to be in match play knock-outs played out over the year. Most single-sex foursomes tournaments are played at stroke play, but there is an ancient (100 years+) one here in West Fife called the Nairn Trophy which is a knockout at scratch for 4-man teams using the "holes up" method of scoring (i.e. you play your match to the 18th, count up the holes up for each team, and the team with a positive holes up count wins the match. It is easier to play than express.
Mention must be made of the BUDA cup events, each of which has incorporated at least one and ususally two foursomes rounds amongst the 5 played, in line with the Ryder Cup format. This normally acounts for 2 of the 5-20 foursomes games I play each year.
Finally, to my knoweledge, friendly foursomes match-play as described by Craig, tends to be confined to a small but steady number of traditional clubs such as Littlestone, Deal, Muirfield and Rye. It is a fantastic game to play if your focus is less on what score you shoot than what camaraderie you can experience and how quickly you can get from the 1st tee back into the 19th hole.
Rich