I'm currently playing a character who was once a deity but was stripped of his power when his world (and thus worship-base) was utterly destroyed. It was interesting playing him as a 5th level character, since he assumed he was still as powerful as he had once been and got into some messy situations because of it (for instance, attempting to forge a replacement sword for himself barehanded in a campfire).
Its a fairly high-powered campaign now, and he's gotten back a tiny shred of his former godhood. It has mostly flavor effects - he can receive prayers in his name, grant 0-level spells to worshippers, and is eligible to take things like Craft(Soul) and Craft(Lifeform) which has led mostly to amusing situations as his creations - a race of stone golem-like beings - are not the brightest of creatures. Due to the power-level of the campaign, being a god isn't mechanically that significant compared to the stuff that gets thrown around by the party, though its nice to not have to worry about natural 1s or antimagic fields.
I've run a campaign where one of the players ended up with the office of what passed for one of the gods of the campaign world, after the party witnessed the being's death while defending a breach in their reality. The result in that case was that he got a bunch of sort of weird mechanics that meant he was extremely powerful in certain situations, but very vulnerable in others. It eventually worked out, but I had to change some of my combat balance assumptions significantly. It probably helped that I wasn't actually using the Deities and Demigods rules though. I don't think I could have balanced around some of the salient divine abilities like Annihilating Strike, Life and Death, Divine Splendor, and True Knowledge. Some of the things are just hard to run like Know Death, which requires the DM to predict the future or lock it in, and the divine sensory ranges.