People often tend to confuse memory (RAM) and hard disk space. I'm not sure which you're referring to, but will try to answer your question.
A faster hard disk can certainly increase performance, if the current hard drive is a slower 4200 or 5400 rpm drive, a 7200rpm drive can help. Upgrading to an SSD (Solid State Disk) can improve performance even further, since it has no moving parts and much lower latency (the time it takes to access your data). Additionally, Mac OS X likes LOTS of free space. So, if your hard drive is full (or nearly full), thinks can start to drag.
Memory (RAM) is often touted as a performance booster, but the reality is that although it can produce the effect of making your computer feel faster, it's really just operating more efficiently if you actually need more memory. How do you tell if you need more memory? Simple, open your most commonly used applications, then just fire up Activity Monitor (Applications => Utilities) and click the System Memory tab. If the pie chart is primarily green, chances are you've got plenty of memory. If it's primarily red or yellow, then you probably want to look at upgrading.
So, tell us a little more about your issue (particularly system specifications, which you can find by going to the Apple menu and clicking "About this Mac") and why you suspect it's time to upgrade. It's entirely possible that depending on the issue, a little basic maintenance can make your Mac feel like new again.
