Many people feel that it's nice to have a 'unbranded' OS. I don't like all the custom software and settings that companies tend to ship on phones. I'd rather stick to having a open source OS as much as possible.
Besides having a 'default' Android experience you do end up with some special features and other things that Cyanogenmod enables.
Also as it's hinted to above, if you have a popular model that is well supported by Cyanogenmod then you can depend on them to produce updates for your OS so that you don't have to depend on your carrioer or phone manufacturer. Even if Cyanogenmod drops official support you can still get hacks and more independently minded variations to install on your phone.
If your in the USA, or other country with a like minded populace, and you choose to purchase a subsidized phone with carrier-branded OS then there is no question about the superiority of Cyanogenmod. No question at all.