I am going to be getting a new HP Pavilion dv3z and don't know whether or not to get 64 bit over 32 bit. What are the main differences? What are the advantages of each one? It would be great if you could be very, very specific.

inb4 "Google", etc.

64 Bit, 32 bit can't use more than a certain amount of RAM (2 GB, ish), which is bottlenecking given that most modern gaming computers will have more than that.

I thought it was something like 4gb... and after that the system still sort-of uses it but not really...
Anyway, 64-bit is also more efficient overall but requires special drivers and OSes, granted most larger companies will have them, but it's still better to check. Anyway, if you're sure everything will work, 64-bit is generally better...

EDIT: Yeah, it's 4gb of direct addressed memory for 32 bit, the rest, as I mentioned above is sort-of kind-of used but not really.

Speedwise, I know that 64 is faster/more efficient. But is it true that some programs don't run on a 64 bit than run on a 32 bit?

4 gigabytes for windows XP professional and 2GB for basic.

Very few programs don't run on 64 bit I don't think... you should be fine, but I reccomend you do some research to figure out if your vital programs work on 64-bit.

The laptop can be either 32 or 64 bit, and everything on it is adjusted accordingly to that. But that's all new stuff. 64 bit programs won't run on 32 bit, but I knew that. So 32 bit should run on 64 bit?

The 2GB limit is for applications in windows.
The 4GB limit is for 32 bit OSes without PAE.
Oddly enough, all OSes after Win 2K have PAE, but Microsoft puts a synthetic limit on the RAM(4GB).
If your processor has PAE, you can get 32-bit linux to use up to 64GB of RAM.

On compatibility:
Some 32 bit apps don't work in 64 bit.
32 bit drivers don't work in 64 bit.
Any thing 16 bit won't work in 64 bit.
There is also the fact that actually in some aspects, 64 bit can be slower running 32 bit apps, with the emulation layer and stuff. It is faster for 64 bit apps, which don't need emulation and can use all of the whatever memory Windows decided to allocate.
32 bit apps will still only use 2GB of RAM.
So, CC can't use your extra RAM. Nor can any 32 bit app.
EDIT:
Add clarification.

I got 64bit vista, Sofar, i don't think iv had one problem trying to find drivers, software, anything