Is there a limit to how tall my Tower can be?

There doesn't appear to be a limit to the number of floors...but there is a limit to the number of floors that have anything in them.

(Based on v2.0 numbers...)

   1 Lobby Floor
+ 63 Residential Floors
+105 Commercial Floors (21 of each of the 5 types)
   =
 169 "Useful" Floors 

However, you can keep constructing additional floors beyond this. You just won't be able to turn them into anything - when you pick Residential or any of the Commercial types, the game will tell you that you've maxed out that floor type.

It's up to you whether you want to blow away millions of coins to add unusable floors from 170 onward or not.

I suspect that there is a maximum of 152 floors in Tiny Tower. This is because there are (as of v1.5) 57 different residential floors + 95 commercial floors. Every time I build a new floor, I get a residential or commercial floor that I don't already have.

The official number given by NimbleBit (emph mine):

There are currently 87 residential floors and 29 floors of each business type. Once you have all 232 unique floors, you can continue to build empty floors. We may add more floors in the future but do not have any plans at this time.

Just as they say here, and the answer by JohnRegner, you can continue building empty rooms.