I know for a fact that GOJIRA could beat your measly Tiger I any day of week!
Ok, so much for humor.
The Tiger I remained a capable vehicle throughout the war, but it was surpassed in combat power by the Soviet IS-II, which was able to knock it out at fairly long ranges, and could withstand a hit from the Tiger's gun at some of the longer ranges. (It should be noted that the Tiger's reputation was such that IS-II crews sometimes ran away when they saw Tigers, even though their tank was arguably superior!)
The Pershing could take on a Tiger on pretty equal terms too, although the beginning for the Pershing as inauspicious, being knocked out by a Tiger I in their first encounter.
Someone mentioned Pershing vs. Tiger II. I don't recall the Tiger II ever fighting the Pershing. Anyone have a specific story of such a battle? (We all know that the Pershing was more than a match for the Panther.) I think that by the time the Pershing arrived, the Tiger II units were largely engaged in the fruitless German effort to prop up Hungary.
The Tiger II didn't really have any serious head-to-head challengers. Then again, as someone mentioned earlier, combat doesn't seem to care much about specs! The first battlefield use of the Tiger II resulted in them being ambushed by T34/85's and the destruction of several Tiger II's.
Some claim that the IS-III might have had some limited WWII usage at the 11th hour, but I wonder if even that vehicle would have been able to defeat the Tiger II in s straight-up fight.
One interesting thing about the Tiger II is that Russian tests indicated that the quality of German steel had fallen so much that the Tiger II's armour was actually weaker than the Tiger I's. Interesting. I wish I could find the source I saw on this a few years ago -- it was a Russian analysis using captured vehicles, which they analysed and then shot to pieces with Soviet armament.
Now on to the next question, could Batman kick Superman's butt?