Operating Systems do get cluttered up and bogged down depending on what you are doing and what you have installed. I see many with Skype and Yahoo Messenger auto-launching, and that eats up resources and causes the machine to take longer to boot. A hard drive that is just about full also makes operation of the computer a lot slower.

It could definitely be the hard drive dying down, and the Smart Utility recommendation is a good one, but if the drive checks out fine, you should try wiping the existing drive and reinstalling first, unless you are not happy with the current amount of hard drive space and are looking to upgrade anyway.

I work all day long with iBooks that have 10GB drives, and a lot of those still work fine after 9 years, so I wouldn't assume the hard drive is bad.

rdklincorporated is 100% spot on. OS X still can get bogged down with things starting up and it still needs to be defragged occasionally.

Check the Login Items tab on your User account to see how many things automatically start up when you log in. See how many you can eliminate. Make sure that at least 10% of the capacity of your hard drive is free space (10G on a 100G drive, for example). The OS needs this to use as swap space and not having that slows it down tremendously.

As doing backups should now be done by everyone, doing a complete erase and install will not hurt a thing and can rejuvenate an older machine.

OS X does not slow down without a reason. Its most likely a hardware issue, such as a failing harddrive, I recommend at least running a SMART Utility

Harddrives have a limited lifespan, and if you are still on your original harddrive, its long overdue for a replacement anyway.