There were hand-coded assembly loops that were 3-4 times faster than x86, using Itanium's predicates and rolling register windows.
But I guess you said mainstream. So unless you count database engines, I suppose the answer is "No."
Today you can get the same vector performance using SSE4 and AVX. Almost all of Itanium's good stuff has been rolled into Xeon.
As far as I know (which isn't very far, admittedly) they only really managed to reach parity with some performance gains over x86 in a few niches, but it's also a bit chicken-and-egg. It never had enough attention to really get the optimization and porting efforts it would have seen if it had been successful.
Was there ever a point in the Itanium's history where there were Itaniums that ran mainstream software with better performance than equivalently priced x64 processors?