The good folks over at The Sweet Setup have written up a nice review of apps to share lists with other people. I've used their top pick, Wunderlist, before but never stuck with it. Maybe I'll give it another shot.
My wife and I currently use Apple's Reminders app for grocery lists, simply because we didn't take the time to install any other options. The iCloud syncing is painfully slow, and for some reason a ridiculous notification sometimes shows up in Calendar saying that she changed 200+ items. Hardly ideal, but being the default app counts for a lot. The Sweet Setup ranks Reminders second behind Wunderlist.