Backing up game save data possible without root?

Is there a non-root free method to back-up save-data?
I have a Nexus one and really like the phone, but I hate that it only has 200mb internal storage for apps (and it would be safe to leave at least 32mb free, so that leaves me with 168 mb only). With Google+, google maps, Adobe Flash, google music and android market all using 7-13 mb, that leaves little space for other apps.
I have put all apps on SDcard as far as I could, yet I am still running out of space. (My SD card has more than 50% free, but the apps can't be put on there or they still use up a lot of my internal storage space)

So I wanted to uninstall Plants vs. Zombies (moved to SD card, yet it's still a 15mb app) but I don't want to lose my save data, because I want to be able to play it in the future. (Best android game for me, so far)

I don't want to root my phone and I don't have a credit card, so I can't download paid apps from the market.
Is there any way I can back-up my save game from Plants versus Zombies (and other games/apps for that matter)?



p.s. That Nexus Prime better be released soon, I need a new phone, one with a LOT more internal storage space for apps!