Phone: Droid X(Android 2.2.1, Liberty 2.01)
To me, in the world of Android grocery lists, there are two major players. There's a few more, but I really don't feel like the android version of grocery king or OI shopping list stand up to these two. So that leaves you with Grocery IQ and Mighty Grocery. While both are target the same audience. And Grocery IQ is free, mighty grocery does have a lot of features, enough that the $3 could very well be justified.
Grocery IQ:
When I started using this, I had a lot of sync issues which turned me off of this. But I recently tried it again, and the sync worked this time around. It's simplified, compared to mighty grocery. Quick lists, easy ui, can share lists between say you and your wifes/husbands phone. Does a pretty good job organizing, ok barcode scanning, and can email list to yourself. Overall, for free, it's extremely useable, and worth the download. The only thing that really annoyed me are the coupons, uses coupons.com service, which makes you jump through a lot of hoops to actually get a coupon printed out.
Mighty Grocery
I was actually pretty satisfied using the free version of mighty grocery, until amazon decided to give the full version away. Even the free version does a great job of auto-categorizing the foods you enter. And it goes well beyond just that, letting you customize the aisles/categories and predefining food to go into which. If you're motivated, you can really strategize the hell out of your shopping trip. Full version adds things like recipes, extends predefined lists, backup, barcode scan, configurable tabs, and screen rotation. Which a few of those actually come in pretty handy. Because of the amount of features, certain areas of mighty grocery definitely take some time getting used to. UI is good for what it is, but you definitely can find yourself getting lost. Having so many options with things like predefined catalogs, recipes, and so many options to share, are the real selling points to me. I can dump lists to facebook, springpad, my email, dropbox, etc. And starting with my previous list is essential for my shopping needs.
Winner? To me, they are both great applications, and grocery IQ being free makes it totally worthwile. But for me, i still love mighty grocery. It's worth the $3. After I took the time to get used to it, i can't go to anything else. Try the free version, compare yourself.