Version 8.1 is 64 bit. Anything prior is 32 bit. If you have a 64 bit OS, 64 bit software will function more efficiently overall than 32 bit software.
If you go to Help --> About Tableau it will say whether it is 64 or 32 bit in the upper left next to the version number.
Also, 32 bit Tableau Desktop shortcuts are labeled as Tableau 8.1 (32-bit).
If you are on a 64 bit machine, you should install 64 bit Desktop in my opinion as you will gain the ability to address more memory due to the bitness. 32 bit programs have a hard limit of addressable memory per process.
I hope this helps,
So 8.0.0 is 32 bit.
Thanks Dan, Toby and Brendan.