Being logged in with your Google account will backup most basic things to the cloud, but not near as much as iOS does. Assuming you have the setting checked to backup to Google things like installed Apps, wifi passwords, device settings do get backed up; although a bit inconsistently in my experience. For picture backups you would need Google+ and have instant upload enabled. Contacts and calendar will sync automatically and as long as when you add new entries you select to add to your Google account and not the local phone memory it will be saved. if you forget and add contacts locally you can always hit the menu button and select "Merge with Google" to upload local contacts.
For me the biggest missing feature on Android is the backing up of 3rd party application save data. It's so annoying to flash a ROM and lose all progress in a game after re-install or having to always reconfigure applications. Thankfully there are products like Titanium backup which help resolve this, but it would be so much nicer if it was built in.