Currently, I have a Thunderbolt, but I'm planning on buying a Galaxy Nexus whenever that becomes available. Thing is, I have a few games I'm playing, and while I know I can simply redownload the games from the market on my new phone, is there any way I can also transfer the save data? I don't want to have to start all the way at the beginning, with games like Angry Birds, Cut The Rope, Symphony of Eternity, etc.
You should be able to use titanium backup to back up the game and game data to your current SD, then install titanium backup on the new device, insert your SD, and restore the games. just be careful not to backup and restore any system apps! Big trouble if you do!
Do as Moscow suggested... I know many/most games don't allow you to save your game data to sdcard so you would have to obtain root so you can use Titanium or MyBackup Root to save your game data on your sdcard and then transfer it over to your computer for safe keeping to restore on your new device. Of course this will require you to root your new device to get that data back.
Small price to pay for all those long hours getting 3 stars on Angry Birds
If sd card transfer isnt an option, theres an easier way with titanium backup pro.
Once youve made a backup of save data, hold down on the save in titanium and click "send backup". send it to something like dropbox or google drive and then redownload it on your device. I did it from my nexus 10 to xperia tablet z, and the nexus 10 has no sd card slot.