I'm making a game which resembles the Sonic the Hedgehog games. I was wondering, what makes them fun?

Also, since Sonic has almost as many haters as loves, I will ask... what could be improved about them?

Here is my own list of things:

Things which make it fun:

Fast speed
Multiple paths
Nice tricks (like running through loops)
Collecting rare, hard to find items (chaos emeralds)
Minigames (those games you play to obtain a chaos emerald)

Things I don't like:

Simple enemy AI. Say you have a bee robot, all it will probably do is shoot a pellet at you.
The difficulty of some of the early games. They were hard.

One common thing I see in games like sonic that make them feel fun is that they have greenery. Green grass, trees, blue skies. Reminiscent of what a kid sees when they are playing outside.

Mario, Rayman, Banjo Kazooie, Minecraft, The first Rachet and Clank, and a new favorite of mine, Knack.

Also, the games are easy to pick up and learn, while still offering enough challenge.

But one thing that makes a game fun or not fun are the game mechanics, like the things you mentioned above. There is a lot of room for originality because many games just reuse the same mechanics and change the graphics.

One thing that made Rachet and clank more involving was the scale of the game. Things like that make you want to explore, as a kid would outside.

All in all, making a game that brings out that "old kid in you" feeling makes games fun. This was the purpose of the creation of Knack. And I haven't enjoyed a game like I have knack in a long time.