.. unless you are considering an operating system upgrade on an old computer, not something that I recommend anyway for anything pre-2006.
All you have to know is that most software is still only 32-bit because it doesn't need to be any better. Software which is graphic intensive, producing large files does benefit from being 64-bit, an example being CAD or video editor stuff.
You will only find a 32-bit operating system on a computer where:
the motherboard architecture is 32-bit
total RAM capacity is 2gb or less
the computer user has downgraded for whatever reason
You will find 32-bit software everywhere, all tried and tested. To be honest, 64-bit software isd still in its infancy, is a major re-write of the 32-bit original, and is generally less compatible with other software.
A note about the installation of software..
Software originally written for Windows XP assumes that the operating system is 32-bit, even though there was an XP 64-bit variant. So, if you try to install some older software on Vista, Windows 7 or Windows 8, it might tell you that it needs a 32-bit operating system. It is NOT looking for a 32-bit version of Vista, Windows 7 or Windows 8. It is specifically looking for XP. This is a good sign that it is NOT Vista, Windows 7 or Windows 8 compatible, regardless of which bit version you have installed.
In this circumstance, you will need to look for alternative software which is known to be compatible.