They're not raw enough, but I think about the closest you'll get right now to the concept of Zep might be the Foo Fighters. It's real rock & roll, the musicians are talented, their front man is ultra-charismatic, and they consistently put out hit after hit. If you want a slightly less rock-ish option (which isn't remotely like Led Zeppelin but meets all the criteria except for specific music genre), it's hard to go wrong with Pearl Jam ... or any of Eddie Vedder's side projects.

To co-opt what someone else said, in order to find what you're looking for from the 90s, you kinda have to go look at bands from the 90s and pray they're still together.