EVE seems to have more players using multiple accounts than any other game I have come across. Witness the responses to a request on the official forums for advice on maximising earnings from PVE missions. Three of the first four respondents admit to using multiple accounts. We are talking about separate paid accounts here each with their own subscription.
My gut feeling is that the skill system is the main reason for the popularity of multiple accounts in EVE. In mmos where character progress is based on playing time it can be very difficult to level a second character without neglecting your main. In EVE the main on a second account can be trained independently with little time investment other than logging on periodically to initiate new skill training.
Having a fully developed second character is obviously a significant advantage either as a source of alternate skills or as a backup in combat situations. In addition to their game play utility alts can play a role in the complex information war that underpins EVE's pvp game. This concept is explored in Nate Combs' recent Terra Nova article: "A Culture of Mistrust in EVE-Online"
While CCP does not officially support multiple accounts it certainly encourages it. In the past they have given special offers to encourage starting multiple accounts. More recently they have implemented patches to facilitate the running of multiple clients on one computer. Why would they not, every additional account increases their subscription revenue.