There's a bunch. The biggest problem you'll have is selecting just one.
I'm really partial to the older Winchester Model 52's. Mine's a Target Model made in 1936 in 90%+ condition. The accuracy of the Model 52 rifle legendary. I would put one with a good bore up against anything currently manufactured. A decent Model 52 is going to run $500 or more. If you've got a lot of money, look for one of the Model 52 Sporters.
In new bolts there's the Sako FinnFire, very nice but pricey.
Lever actions, The Marlin suggested is a great rifle, but there's the little Browning BL-22 as well.
In semiauto, Ruger's 10/22 is the standard, and again there's the Browning that is a great little rifle. (If your a purist look for the Belgian)
If you want a great inexpensive .22 bolt action the Dan Wesson Coyote Classic is top notch. Mine was delivered about 1 month ago. The fit and finish are superb. It shoots well too. I got one from the first production lot, neat having a rifle with such a low serial number.
I could go on but others will be along to offer up other ideas as well.
Enjoy your search.
Take Care