For me, I maintain multiple accounts for several reasons.

1) Differing program partners - mainly non-airline but sometimes airline as well. Coupled with this is differing reward values for the same (non-airline) partner. My standard example for Skyteam is: Barnes & Noble purchases - I can get 5 miles per $1 with CO, but only 2 per $1 with DL & NW (that's the whole reason why RewardsDB.com came about after all). The same holds true for many other partners (although it isn't always CO with the best rates). Other examples are: Randalls here in AUS gives CO or AA miles only, CokeRewards only gave DL miles, e-rewards only allowing one 2,000 mile redemption per year per airline so you end up getting miles in several different programs, etc etc.

2) Redemption - its always easier to get a reward seat with the airlines own miles than with a partners. Also the amount of miles needed for certain awards sometimes varies between partners or there are awards no available to partner members. And of course the differing airline partnerships mean that there are some miles that can be used for a certain flight/partner and some that can't - look at HNL-SYD on HA as a redemption option for SkyTeam, not all of them allow the redemption at all.

3) As others have mentioned, a big earner relates to credit cards - both bonus miles and having both credit and debit cards. DL doesn't offer a debit card which both NW & CO have. Different bonus offers often make it worthwhile to get different cards - take the US Airways Mastercard promo for 2 free years and 1.5 miles per dollar, depending on your spend a far more attractive offer than any of UA's which were all 1 mile per dollar or worse.

4) Bankruptcy. As someone who lost miles when Ansett collapsed (but thankfully had most of my miles in UA since I got status from work for them and more bonus miles) it is tempting to spread ones exposure by having miles in multiple programs. Also is a partial shield against sudden rate hikes.