Utility / Cook's knives run 5 to 6 inches in blade length. Paring knives are similar but smaller and shorter (3-1/2 to 4 inches). Some specialty paring knives are as short as 2-1/2 inches. I don't own a paring knife and don't miss it. I do my peeling with a swivel peeler. Decent utility knives can be had from about US $10, and on up to whatever you might want to pay.
Shown in the photo is my ancient Sabatier utility knife. This knife has the form of a forged blade but it's fake, the bolister is cast onto the blade in a mold and is probably aluminum, but it does add useful rigidity. The blade is of a good knife quality stainless and has held up to decades of severe abuse.
I use this knife when I need something narrow and pointy, but in truth the main uses it gets are cutting open boxes and slitting the capsules from the necks of wine bottles. Still, when you need something like this you need it, so I wouldn't be without it. This knife is 5 inches long on the cutting edge, 9-1/4 inches long overall and the back edge of the blade is 0.06 inches (1.5mm) thick. Actually it was originally about 1/2 inch longer but someone used it to pry and broke the tip off, so I had to reshape it.
More on Knives.