Pros? They're usually quite accurate, accessories abound (if you're into that kind of thing), with a collapsible stock they're adaptable to most shooters (including youth)
Cons? Unless you're talking about the AR-10 platform, you're limited to what most of us would generally consider "varmint" cartridges, with the possible exceptions of rounds like the 6.5mm Grendel, 6.8mm SPC, or .30 AR (though you can make a big jump in shorter-range power with rounds like the .458 SOCOM or the .450 Bushmaster). They do tend to be heavier than their bolt-action counterparts. They're not the easiest to keep clean.
I tend to prefer bolt guns and single-shots for hunting, but have used the AR (in .223) on a number of occasions to bag coyotes and a couple late-season Thanksgiving dinner turkeys.