I just got a new Shimano crankset and it has this plastic ring on the "inside" of the small chainring. I'm thinking that this just some packing material. Am I right and can I toss it, or is this a real part?
I haven't seen one of those before, but it looks as though it could stop the chain dropping between the bottom bracket shell (the bike frame) and the crankset if you ever drop the chain off the inside of the small ring. When that happens it can be tricky to get it back out, and if the chain is oily you end up with that oil everywhere (mostly on your hands and clothes). This is something I see occasionally, as I stop to help people standing next to their bike looking helpless on my ride to work. On some bikes it's possible to get the chain wiggled in such that it's still movable but you can't get it out without taking the crank off (I've seen that in the bike shop).
I would leave the plastic ring in place just in case is stops that happening. It's one of those "5 grams stops the once in 10 years problem" things.
It might also reduce damage from the chain rubbing on the frame if the chains falls off as above.
Edit: after Batman found the part (Shimano EV-FC-M410-2465A), here's a diagram of something very similar via this pdf link