I formatted my PC and reinstalled Windows. I didn't backup my files. 

Is there a way on Steam where I can retreive my saves and continue from where I stopped? Or do I have to play everything from the begining again?

im pretty sure steam keeps your saves

If you had cloud saves enabled then most games support that and you should be able to pull down your saves. You probably should have backed up your saves lol.

If your saves were on the Steam cloud, they are all there, if not then you're basically fucked...

Same thing happened to me last year, I lost all my saves but you keep your achievements and hours logged on Steam.

The only thing that was on my computer before deleting everything was Steam and the games. I thought I don't need to backup since I can download them again. Totally forgot about save files.

If the game has cloud saves and is activated (which is the default)

Not all games have cloud saves, especially older games. 

You will be able to continue your progress on games that have the cloud. You may have to import the saves, I'm not sure.

For the games that don't have the cloud, you are out of luck. You can check if a game has the steam cloud by looking at its properties, or going to its store page.