You can definitely play EVE solo, doing contact missions and mining to your heart's content. You can't ever NOT be in a corporation, though, even from character creation, but there's nothing that says you have to go off on your own player corp. Granted, as with CoH, there'll be some things that you can't do if you don't team up or join a player-run corp, but I've not gotten that far into the game to decide if I miss it or not.
The other thing that's nice for the solo player is the real-time character progression that continues when you're off-line. It lets you train even when you're not logged in, so there's less of a sense of having to run in teams (fleets) for "mad eXPees." As long as you've got skills training in your queue, your character's advancing right along with everyone else. (Granted, you do have to purchase most skills before you can learn them, so you'll still have to be doing something in-game to be able to pay for them.)
The one thing EVE doesn't do is encourage you to create alts in the same way CoH did. You only get three characters per account, and only one character per account can be training at any given time. EVE's solution to that is encouraging having multiple accounts, which was talked about up-thread. Since any character can learn any skill, it's up to you to decide if you want separate characters to specialize in different areas, or if you want to be able to it with just one.
If you decide you want to check it out, PM me your e-mail and I'll send you a buddy code for an extended trial period.