Makes a big difference whether you are thinking last 5 years or since 90s.
I think most critics would tell you Nirvana for early 90s and Radiohead for late 90s. Nirvana is already iconic viewed today. Some other banRAB thrown into the "influential" mix would probably be Blur, Smashing Pumpkins, Weezer, Rancid, Pearl Jame, Rage Against The Machine, Marilyn Manson and Nine Inch Nails.
If you are talking about iconic figures in pop and country music, the 90s and onward had some of the biggest in history actually, and some of them not necessarily lacking in musicianship. Some super divas: Britney Spears, Mariah Carey, Shania Twain, Sheryl Crow (9 Grammies!), Shakira. Madonna and Janet Jackson were in their 30s then and still very big.
On the rap front I think Jay-Z and Eminem, Outkast, Dr. Dre, are all going to be remembered as some of the most influential.
I am not knowledgeable on music of the last 5 years though, so I don't know if any of the young musicians out there is iconic or will become iconic. But Radiohead is still very current, and they are already in Rolling Stones' "100 Greatest Artists Of All Time" list.