Most of them are not hosted here, rather in Relic Castle or PokéLiberty (which is in Spanish), but I love short fan games a lot too! I recommend to you a few funny ones:
-(broken link removed) by Hukon. You arrive at a festival in celebration of Jirachi, only to have to foil the plot of some loser called Chad the Dark Lord. There's a lot of flavor text in between, a variety of Pokémon to build a nice little team with, a lot of events, and even a Game Corner! I've never found another game quite like this one again in my 4-5 years of playing fangames. Oh, and your player character's parents were totally
not kidnapped... but that's another story for another day.
-(broken link removed) by Tomix9tomix, Ranko, Vendily and Lichenprincess. This one centers exclusively around a fishing minigame. If you have patience, it's really rewarding, just for the WTF factor of some of your catches and the side-splitting PokéD--- I mean Big Book of Fish entries.
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Psyduck Hunt by Kyu, Kid, Clara and Caeles. Not sure if this one counts as a short fangame experience because it's an arcade-like one, but it's a great remake of Duck Hunt with Psyduck as the target. Oh, and there's no dog Pokémon laughing at you, which is a big plus. (Not as of this version, at least.)
-(broken link removed) by Voltseon. Another Pokémon-style remake of an arcade game - Toader. Get all the Politoed home, or they won't like what they see!
Hope you give them a try! I really liked all of these, and if I come across any others, I will list them here as well.