Worlds you were proud of, you could show to your friends, you spent a lot of time on it, etc (on survival of course), but you lost for some reason
I had 3 big worlds, the first one was in the jungle and there was this house in a mountain with a huge village i build not so far from there, with houses, farms, stores and A LOT of villagers (which i cheated but only for the eggs). There was also this huuuge villager statue which i spent a lot of time building.
The other one was one of my first world ever, it was a small island with a big wooden house, towers and a automated cactus farm (which i added later on- it was probably my biggest redstone creation)
I would be very curious to play on my old worlds again, i forgot almost everything (it was 3 years ago, i changed computers and all, so)
The last one got corrupted for like 6 months and only last week it worked again, it is a huge survival island, very proud
I miss my very first world. In mid-2011 during Beta 1.7.3, I was brand new to minecraft. My neighbor, who started playing during Beta 1.2, taught me nearly everything, and helped me get started by digging out a little enterance for a home in the side of a cliff.
I expanded the home once I had everything figured out. The home was multiple stories and was in the side of a cliff near a massive land arch. There was an enterance that had a fireplace, then above with a bedroom/storage area, and on top was a small area used as a watch tower of some sort so I could view the land from above the arch.
Outside was my nether portal, farm, and this one redstone contraption, although I forgot what the contraption did.
Honestly, it was probably the time I was most productive on Minecraft Singleplayer. Now I am mainly found on servers.