Bivy- best to use in high winds in a dusty desert and it's light weight
Do not use with alcohol. You will piss yourself when you can't find the zipper while drunk.
Very claustrophobic and the bivy- is constantly touching you face and it's hard to breathe.
Tarp- never... Bugs, poisonous spiders, scorpions, poisonous snakes.
Hammock- warm nights, super light weight
Less bugs but it's still a possibility if you don't have a hammock with a built in bug net
Tents- rain, snow, bug infested areas or if you want to maximize your chance of getting a good night's sleep