Champions Online, and its sister game Star Trek Online. CO, at least, allows you to play through the entire game without ever giving the publisher, Cryptic Studios, a single dime if you don't want to. You get two character slots for free, can choose from nine Archetypes (premade character progression templates, which can be individuated at certain levels), and have access to a pretty fair selection of costume parts for your superhero.
(In case you're interested, here's a quick look at the characters on one secondary account. There are three because I got one free slot for playing during last November's anniversary event.)
I don't know for sure yet if STO lets you play all the way to the rank of Admiral for free, but I don't see why not, given how successful the method has been for CO. You start with a Miranda-class light cruiser, pick up two bridge officers during the tutorial missions, and get to do some cosmetic modifications for free as you start. (The USS Belleau Wood, commanded by Lt. Jon Sills, looks nothing like the USS Crazy Horse, commanded by Lt. Draken Darthmal [my roommate], for instance.) Like CO, you get two character slots for free. You also get new ships when you get later promotions - Draken apparently made LCDR today, and was rewarded with an escort cruiser, the next step up.
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Sodium is a metal that reacts explosively when exposed to water. Chlorine is a gas that'll kill you dead in moments. Together they make my fries taste good.