It depends. But first things first. Did it just suddenly get really slow? Danger, Will Robinson! There's something seriously wrong, and the first thing you need to do is backup all of your stuff to external media. But if it's been a gradual slowing you can relax a bit. There are any number of reasons why your computer may have slowed down over time. With Windows machines in particular there seems to be a gradual buildup of what I think of as electronic silt, or sludge, that can slow things to a crawl. This can happen so gradually that you don't even realize it until one day you notice that you can make yourself a cup of tea and scramble some eggs for breakfast in the time it takes to open a spreadsheet.
There are a lot of software products on the market that claim they will speed up your machine. Don't fall for their pitches. Many claim to speed things up by cleaning out your "registry". This is so dangerous that I get twitchy just thinking about the damage you could do by attempting it. Registry editing is something best left to the pros, believe me. It's a mistake I've made more than once.
Some people will tell you all you need to do is "defrag" your hard drive. If only it was that simple. I've done that many times, and the speed increase was minimal.
The best thing to do is to reinstall Windows (notice I'm not addressing Mac users? That's because the Mac OS rarely silts up like Windows does).You'll need to back up all your files first, because what you'll basically be doing is erasing your hard drive and then putting things back to the way they were when you brought the machine home. It's the only sure way to get things humming along again. It's a bit complicated, so you should probably call your nearest geeky friend or relative and ask them to help you out.
But back to the sudden slow-down scenario. It could be that something is about to fail on your computer. So be sure you keep backing everything up to external media while you're waiting for the other shoe to drop.
Or it could be that you've acquired some sort of malware, what people call viruses and spyware. If that's the case, the fix is the same as for the silting problem, because the only sure way to get rid of malware is to reformat your hard drive and reinstall your operating system. Again, there are a lot of products on the market that claim they will remove malware. Sometimes they will, sometimes they won't. The problem is that you can never be 100% sure that your system is clean. The programmers who create malware are clever and relentless, and once your computer is infected there's always a chance that the removal tool you've used didn't catch every last bit of nasty code. So you need to wipe the drive. Sorry.
So, you shouldn't need to get a new computer just because yours has slowed down. It just needs a thorough cleaning. But if you were asking the question because your computer is older and you're looking for a good excuse to get a new one, go for it. I'll help you with the shopping.