Kodachrome is a popular brand of slide film, available in 25, 64 and 200 ASA speeds. K25 is one of the finest 135 slide films available with stunning details and wonderful but subtle colours (unlike Fuji Velvia!). The disadvantage is that you'll usually need a tripod as it is so slow.
K64 is a reasonable compromise, but K200 is a bit grainy and dull for my liking.
These films usually (in Europe, at least) come with pre-paid development envelopes to send the film to your nearest Kodak lab. Kodachrome uses its own development chemicals and process; development isn't something most high street labs can do.
UPDATE - it's not Mama you need to worry about (see previous write-up). Kodak have recently announced the discontinuation of Kodachrome 25, much to my annoyance.