A 32-bit operating system is limited to 4 GB of memory ( you can only reference 2 ^ 32 = 4GB ). However, 32-bit Ubuntu is limited to 3 GB. If you are considering between 32-bit and 64-bit Ubuntu and you have more than 3 GB of memory that should be a simple decision.
There is a workaround however if you are still not convinced 64-bit is the way to go - install server kernel as it has support for upto 4 GB. But think about the future when your 4GB will not be enough and you add more memory?
kerneltrap.org has a good page on kernel and high memory with a good explanation of physical memory versus virtual memory.