There could be a number of things affecting a computer performance as it ages, here's a list.
Recent drivers installed
Some times you can have drivers that degrad performance, just make a note if you recetly updated any hardware drivers and if not dont worry about it then.
New Hardware recently installed
If you installed any new Hardware recently then you need to check and make sure its compatible with current hardware and make sure it is not causing any problems
Hard drive
HD failing - if your computer HD is failing you will notice a huge performance decrease followed by clicking noises depending on the severity. I would suggest check with your hard dirve company and see if they have any diagnostics tools to check HD health.
HD too full - If your hd is full over eighty percent capacity. I would suggest clean up and make room on it.
Windows
Ever so often windows just need to be reinstalled, so if its been a couple of years as suggested earlier try doing a complete reformat and clean install.
The undeteted Virus
Yes when I had a shared computer with my brother and sister ; every so often, I recall geting a virus norton didnt seem to notice at all.
I wouldn't suggest trying to manual clean it up yourself because its a pain even when you know the memory names of every single windows resources and programs installed. Just if its a shared computer and you suspect some one visiting unsafe sites or downloading unsafe files. I would just reformat and install windows.
Tips for computer troubleshooting
Check your windows event log files, look under applications and system and look for anything you see in red or yellow.
If you suspect faulty ram do a memory diagnostic
Make sure you do not have too many startup programs, If so just go to start menu, under run type in msconfig, uncheck some programs you do not need to upon boot and restart windows.