Lynch
Here for the cookies and the tunes
Black Stone Cherry was the first band to come to mind for me. I've got both of their albums and really enjoy their stuff. Hell of a good band. I hope they are around for years to come.
Another band that came to mind is Godsmack. I don't like everything they've done, but I do like a lot of it.
Alice in Chains would be my #1 choice if we were simply talking about bands who's first album came out within the past 20 years (Facelift came out in summer of 1990, so its still under 21 yrs), but they formed in like 1987 or so, so I guess that they don't count.
Oh yeah, hate me all ya like for this one, but I forgot about Nickelback. I'm certainly not a die-hard fan, but I'm certainly not of the belief that they are a bad band. You don't have to be complex or break out of a mold that works for you for me to be a fan. Never been to a concert of theirs and probably never would, but I do like a fair amount of their studio work.
You can also add Kid Rock to my list. I love how he's transformed from what he was in the mid 90's to his breakout release in Devil Without a Cause, on through his next few albums that broke more away from the rock/rap and more into a southern rock style, yet still keeping his raw edgy-ness from some of his earlier stuff.