I havn't used it myself, but
Remember The Milk used to get a lot of good reviews, and is cross platform, with a website to back it up.
Some other suggestions, for a bit more than to-do lists.
Back when I had both Android and iOS, I used Toodledo. There apps for both platforms and a web interface. Lots of features.
Todoist is another, similar, service that I've heard good things about, but never used myself.
Evernote can be used on both platforms. While not specifically a to-to list, it's easy to make notes that have checkmark list. You can also treat entire notes as todo items, with reminders and such.
All are overkill for a grocery list, but pretty much any cross platform todo app you're likely to find will be. It's a lot of effort to make things cross platform, and developers seem to be loath to go to that much effort to sync simple lists.