The best way for you to figure that out is load up everything that you plan on doing "at the same time." Meaning, if you regularly have 5, 10, 20 or more browser windows open, Email client, a media player streaming music/video, a game or high powered editing software, fire that all up! After doing so, hit CTRL+ALT+DEL to open up the task manager and determine how much memory all of your applications are using.
With Windows Vista and Windows 7, this is listed at the bottom of the Windows Task Manager as "Physical Memory:" and is shown as a percent.
For example, if all of your applications and OS are taking up 256MB, or 25% out of your available 1GB of system RAM (and notice I am NOT including virtual memory availability), you should be fine and MAY not notice any improvement with additional RAM. Again, this depends on your needs and your perception of a speedy system.
If, however, your system is using 1.5GB (1500MB) of memory and your system only has 1GB of physical RAM, then virtual memory is being utilized extensively and it would be best to upgrade to additional RAM. How much do you need? Depends on your wallet.
In all cases, the more the memory the better. However, a "gotcha" exists:
If you are using Windows XP, Vista or Windows 7 32-bit versions, they only support a maximum of 4GB physical RAM with, depending on hardware, between 2.5 and 3.5GB available for use by the OS. As such, if you have 3GB of memory and wish to upgrade to 8GB, it would be pointless while using a 32-bit OS as it will not "see" it or use it, anyway.
If, however, you are using a 64-bit OS, this particular 4GB barrier does not exist, so upgrading from 3GB to 8GB, depending on system use, may have an effect on your perceived system speed.
The "minimum" RAM to run XP SP2 is listed here:
http://www.microsoft.com/windowsxp/sp2/sysreqs.mspx
64MB is low and any memory beyond that, up to the 4GB 32-bit barrier, would be better. What and how much you need depends on your wallet and the system hardware itself. Check with your PC manufacture for specifics on how much memory your particular model PC supports as they are all different.
The "minimum" RAM required to run Vista is listed here:
http://www.microsoft.com/windows/products/windowsvista/editions/systemrequirements.mspx
Even though it is listed at 512MB for Home Basic and 1GB for all other versions, my performance requirements are beyond the "minimum" and I would recommend no less then 2GB to run Vista at all. By default, on a system with 8GB of memory, due to caching and various other Vista mechinisms, the OS uses about 700MB to 1GB. Using less physical RAM may reduce that figure, but adding more RAM will increase system speed if only making the minimum requirements.
The "minimum" RAM required to run Windows 7 is listed here:
http://www.microsoft.com/windows/windows-7/get/system-requirements.aspx
Even though it is listed at 1GB for all versions, my performance requirements are beyond the "minimum" and I would recommend no less then 2GB to run Windows 7 at all. By default, on a system with 8GB of memory, due to caching and various other Windows 7 mechinisms, the OS uses about 700MB to 1GB. Using less physical RAM may reduce that figure, but adding more RAM will increase system speed if only making the minimum requirements. If anything, make the jump to "64-bit" and get a system with atleast 4GB, if not 6GB or 8GB. You can never have enough RAM.