I recently enjoyed a mix of tomatoes at various levels of ripeness; the taste of the ripe and almost-ripe fruits was delicious, I know people do this with mango, have you found the same?
I like bananas when they are relatively fresh and just recently not-green. But I also LOVE banana bread/cake with very very old bananas in them for their delicious flavours.I wouldn't eat a very old banana by itself though!