Gee, where to start? Union Pacific? (over 150 years without a name change, first transcon) Pennsylvania? (Standard RR of the world) Baltimore & Ohio? (loads of history, one of earliest US railroads) Fan favs not mentioned...
Legomanbill's got a picture of rolling stock from one of my favorite railroads even though it was an interurban line. Another one is the GTW RR. I grew up watching and hearing their trains. Now I live about 150' on the other side of what was the GTW RR main, now the Hayford siding or Hayford. A lot of NS trains use this as a secondary and the the CN is doing major track work on it.
It depends on how you measure the term 'great'. And is it a current railroad, or a fallen flag? For current railroads, I would have to agree with Boxcab and say most likely UP, or Canadian Pacific. CN may be big, but they are also bad and not so great. If it was a fallen flag, then everyone knows it would be the Milwaukee. As the saying goes, "Everyone has two favorite railroads, and one of them is the Milwaukee Road."
I think there is a certain element of truth to that, the Pennsy included. I do not and never have lived even remotely close to any former Milwaukee Road rights of way and I was born after it was gone. However, I do have an appreciation for both the Milwaukee Road and the Pennsy as two major carriers, both of which were legendary through their innovation and their PR campaigns.