So I am on a pretty tight budget (like a lot of folks) and I have a VPS running using Centos v6.0 x86. It has 1024 MB of RAM. I have Apache 2 and MySQL running. I recently upgraded to the latest version of MySQL and after restarting found that my RAM usage went from 14% to 48%. I only have 1024 MB of RAM installed in the VPS but thought that would be enough. Is it normal to see this amount RAM usage even without any traffic? Thanks.
Your usage pattern determines what you need, and you haven't told us anything about that. For example, my personal VPS server has been running for several years with a mere 64MB of RAM. You can bet that's at 100% utilization all the time. It's still very responsive. I answered a question yesterday for somebody who was running with 256MB: Server hitting high loads and becoming very slow. His configuration was just using more processes than needed.
You don't detail what memory usage you're talking about either... is idle free memory, or is it free + cache? Remember that MySQL has settings which will determine consumption of real system RAM.
If you're having regular idle time, 1G of memory may be far more than you need.