I remember the original Thunderbolts, a bunch of villains, just chilling and reading fan mail or going out shopping or finding clothes for Jolt. Even when they went on the lamb with Hawkeye, they found time to have relationships and get side jobs or attend school. Does anyone have a personal life these days? I know few, if any, are shown anymore. Daredevil used to have a great balance between his personal life and super heroics. That's gone by the wayside with Shadowland, but was still an integral part up until a few months ago. Wolverine: Weapon X showcases Wolverine's personal life fairly often with him and Steve Rogers having some beers to celebrate his return or just introducing everyone to his newest girlfriend. Secret Six has had the team go out for a night on the town here and there and showed them having downtime between missions, too, and they make for some of the best issues in that series. These are only a couple of examples, but I was having a lot of difficulty finding more to balance this post out.
Going hand in hand with a character's personal life is their supporting cast. The majority of supporting casts these days consist of other heroes or super powered people. Continuing with previous examples, look at Spider-Man. With no job, no wife, and no family, he's pretty much cut out his entire supporting cast they were attempting to build for him with Brand New Day. There's no reason to see Jonah or the Daily Bugle/Frontline staff. There's no reason for him to be with a girlfriend or potential girlfriend since a super hero, Black Cat, is his on again, off again flame. There's nobody in his life that isn't super powered other than the random Aunt May appearance (like 2 pages in 8 issues or so). We only know most of these people because they've existed for 60 years and if they were new, they became caracitures more than actual people you cared about seeing, like his irratic roommate, Michele, or the snarky reporter from Frontline, Norah.
Another example from above is Green Lantern. Show of hands, who remembers Hal's brother and his family? They had some build up in the early issues and played a small part in Sinestro Corps War if you can't recall. They were rolled out for a random shot during Blackest Night and that's the only time we've seen them again in like two years. Ferris Air or the people that work there? Anyone remember them? How about his girlfriend, Cowgirl? Anyone remember her? Hell, Carol Ferris had to go and get a Star Sapphire ring and floss bikini to get some screen time. The entire supporting cast consists of super powered people with multi-coloured rings these days. They are more an extension of the story than an actual supporting cast.
Again, with the lesser known characters that can't support titles, their entire supporting casts cease to exist. Blue Beetle was like a modern day Spider-Man in my eyes. His family was an amazing and supportive pillar for him. They no longer appear in any comics to my knowledge now that Blue Beetle is only showing up in Teen Titans. Manhunter's family and supporting cast was another great group of characters with personality and, while they had a few appearances in the 8-page back-ups for her, they are pretty much non-existent when it comes time to roll Manhunter out for a random guest appearance.
Ultimate Spider-Man is probably one of the few comics I've read that manages to balance between action, personal life and supporting casts. No small feat with such a large cast of super powered people, but they'll go to jobs, on dates, to school or just hang out at Peter's place between the assorted battles and super villains they run into. The characters come first in that series and it shows in how much you care about each one of them.