I got that red wine stain out of the carpet!
I sprayed the spot heavily with hydrogen peroxide and then generously sprinkled it with baking soda. I meant to leave it for 20 minutes, but I forgot about and came back 1.5 hrs later. I picked up the baking soda with a spoon and lightly scrubbed away the rest with a cool, wet rag. I couldn't believe it, but the stain was gone. The next day, when there was better light in the room and everything was dry, I could really see that it was gone! (Also, it had not been bleached by the peroxide either.)
I wanted to share this in case anyone has an old stain they would like to try this on.