Wasn't sure which forum would be right for this. But I'm looking for a recommendation for a pellet gun for small game such as rabbit, squirrel, and rat. I would prefer spring loaded or air powered over CO2.

I own two Webley break action guns.  

The Vulcan is .177 and I bought it over 25 years ago.  Still running strong.  Good for birds up to crow size, within 20 yards or so.

My Patriot is .22 cal, and puts a hurt on anything I shoot.  It has killed a number of possums, coons, and thousands on barn pigeons.  40-60 yard kill shots on pigeons are challenging, but fun.

Go .22cal if you are thinking of anything larger than starlings.  Buy good pellets as well.

What price point are you looking at?  Some air rifles can cost more than true firearms, and I have watched some videos of the large caliber ones being used on hog hunts.  But for small game and pest I would also suggest a Gamo, some of theirs are pretty good prices (such as the Big Cat.)  Look around, most gun shops also sell a few of the more common air rifles as well.  But yes, definitely go with .22, I wouldn't trust my .177s with anything other than the gardner snakes I use it to get rid of (they like to nest in the retaining wall around my pool and are a nuisance, its not fun finding them in the pool skimmers...)

Ruger Airhawk and pointed pellets at 35 yards.  Killed 4 reds so far with it from 15 to 35 yards with it and all died immediately.  Hit em in the vitals or head and you dont really HAVE to use a .22 caliber.

I just shot my Benjamin Marauder .25 for the first time today.  One shot at ~15 yards makes it almost the entire way through a very thick phonebook.  The second shot goes in to the same hole due to accuracy and even after hitting the other pellet, manages to come out the other side with enough energy to put a 3/8" deep dent in plywood.  May not be very scientific review, but I was very happy with my first experience.

If you are only looking at small game, then .22cal should be plenty of delivered energy with better availability of pellets and more shots per refill.

When sighting it in, I was shooting 5 round groups.  Except for a single flier (my very first shot), I had 3 holes in the target out of 15 pellets.  The accuracy of this gun is not exaggerated.

Of course, it isn't the cheapest air rifle on the market but is a damned good gun for the money.