This is a list of the things you can currently unlock in Crazy Party for gems. The specifics for how to get each of these to show up is not shown here because I'm just not sure about it. As far as I know as long as you play the game without cheating and progress normally when you have the gems they will show up.

Rewards List

play one unlocked mini-game (1 gem)
Early on
Note: You can pay one gem then play the same game 1 or 1,000 times and it cost still just one gem.

launch a solo micro-game party (1 gem)
Early on

launch a training battle party (2 gems)
Early on

launch a solo mini-game party (8 gems)
Early on

play a micro-game (4 gems)
Early on

unlock the hardcore mode (50 gems)
After having 50 gems or maybe a few more

unlock the custom settings for the online battle parties (250 gems)
Shows at 250 gems.
Allows for custom turn amounts and picking health amounts.

unlock the custom settings for the online mini-game parties (500 gems)
Shows at 500 gems.
Allows for custom game lists as well as custom turn amounts.

Try and unlock mini games, 20 gems
This should be unlocked after completing and unlocking all of the worlds. If you have 20 gems it should show up, but is not for me personally so I am not sure on what exactly makes it show up.

Buy Boards: the deep water : 70 squares, 15 gems
Shows at 15 gems.

Buy Boards: the mystic cave : 81 squares, 20 gems
Shows at 20 Gems.

Buy Boards: the mischievous castle : 90 squares, 25 gems
Shows at 25 gems.