I got a Savage .17 for christmas and it seems that at least one shell out of every clip I shoot will be get hung. What are the reasons for this? How can I fix it? I was thinking that maybe the firing pin was hitting it too high but my friends hits in the same place. Thanks

First, what do you mean by hung? Do you mean not firing the round or hanging up in the magazine? If its not firing a chambered round, it could be the ammo. Are you guys using the same batch? The firing pin is supposed to hit on the rim of the case (rimfire?). How do the indents on the rims from your rifle and your friend's compare. If yours is not as deep, you could have some crud in your bolt. Take it out of the rifle and give it a good spraying with gun degreaser or carb cleaner, and if you have an air compressor, blow it out good, then re-lube with a spray gun oil.
If its hanging up in the magazine, try buying another magazine, you should have an extra one anyway. If it doesn't hang up with the new mag, you can chuck the old one or call Savage and ask them to replace the original.
If none of the above solves your problem, you'd be best advise to call Savage up for the next step.

my bad for not being clear. After I shoot the spent cartridge stays in the chamber. I have to pry it out with something

I've never had that problem. Could be that the extractor is defective. Check out Numrich for a replacement.

Usually it is one of two things. Either a bad extractor or a dirty chamber.

A bad extractor simply doesn't get a good bite on the rim of the case. I just had to reshape one on a Ruger 22 mag to get it to pick up the rim and extract the case.

A dirty chamber could be anything from rust to packing grease or dirt. Just give the gun a real good cleaning. Especially if you didn't clean it when you got it new.

First thing I would do is dump that and get yourself a good cal..
The 22Mag is far better than the 17 ever will be..Use it for
a boat anchor...

Just to reiterate - give your bolt (and bore/chamber) a good cleaning. If that doesn't work try different ammo. If still a problemcall Savage. johnny2 - apparently you never owned a 17HMR. Everyone I've shot or seen shot were super accurate. And that is the fun in shooting them. I've taken 2 turkeys with mine and a bunch of squirrels. And just to be fair using on squirrels, to give them a fighting chance, I limit my shots to head shots only. And its almost too easy out to 75 or even 100 yds. Try that with your 22WMR.

From what I have seen and read..The 22 Mag will out do the 17 cal
At 200 yards a 22 Mag bullet will pass through a grapefruit..The
17 will not..This is only from test I have seen..I am not yet sold
on the 17...

must be a bad extractor, it does it right after cleaning

What kinda of ammo are you using? My savage didn't like Hornady ammo but had no problem with remington or federal - just a thought