Some of the weird fruits you'll find downstairs at my favorite fruit store, the Sun Moon:

Buddha Fingers. Really strange looking. I was going to try this but it turns out they're all rind and no fruit, and so are only used for cooking and display.
Jambu. Like mini pears. Haven't tried yet.
Dragon Fruit. Very strange. Tried this in Vietnam and it tasted like kiwi fruit. Tried it back in Singapore and it didn't taste like anything at all.
Mangosteens. Haven't tried these yet.
Breadfruit. These don't look edible to me for some reason.
Jackfruit. Same with these.

They don't sell durians, unsurprisingly. These are the infamous delicacy that are widely banned from trains and hotels because they stink so bad. They have them in open air markets, and you immediately know it when you walk by a place that's selling them. (Marjorie and I have been known to accuse each other of smelling like durian.) I've tasted it before, back in Atlanta; an accurate description I heard was that they taste like orange custard soaking in toilet water.