I will not give an opinion on Arcade shooters, since this genre, along with FPSs, I cannot seem to be able to play them for more than 5 minutes before I start bleeding from every orifice in my body, meaning, they bore me to death.
Platformers are a different story, these can be extremely fun and addicting, but also can make you wanna skin yerself alive. I like platformers where there's a sense of advancement, getting new moves, new skills, etc., that kinda stuff, you know. These sort of platformers weren't very popular back in the old days, usually they were very straight forward and simple. If you are going to make a simple platformer, make it short, same length as the first Mario for the NES is perfect for this kind of platformers. Keep it fun though, give interesting power ups and stuff like that. You can also make it longer like this but this takes a lot more effort, one my favorite long platformers is Yoshi Island. The game was relatively long for a straight forward platformer, but it was fun and interesting, many puzzles and secrets.
If you plan on making the game reward you with upgrades and/or level ups (beside the typical power ups), you should make it longer. When you add upgrades and levels (character development levels), maybe even different equipable weapons, the game becomes a candidate to be long, but also more technical in nature, these are the ones I like to play. You don't have to have a great story for any of those two genres, although, platformers with RPG elements usually tend to have stories.