Jay-Z is good, but definitely not the best rapper alive. There are a lot of rappers that are better than him IMO.
There's Nas, AZ, GZA, Ghostface Killah, Ice Cube and groups like The Roots, Atmosphere, EPMD.
Of course everyone has different taste, so there's no definite *best*. I have friends thinking Lil Wayne is the best rapper, and I've also heard Akon

. I just hate it when people think rap is all about sex and the like.