Q: How can I "clean up" my IMac so that it runs faster?

Whatever you do, do not download or install any product claiming to magically "clean up" or "speed up" or "optimize" your Mac. Without exception, they will do the opposite. If you already did, you found the problem. Fix it.

If it is only Web browsing that seems to be slower than it used to, that is often the result of such sites becoming ever more demanding of hardware and bandwidth. Short of paying for faster Internet service, buying additional memory, or a faster Mac, there is little you can do to cope with such so-called progress.

If you are experiencing general slowdowns or "freezes" unrelated to Internet activity, the problem may be related to your computer or the software you installed and is something you may be able to fix, or at least improve. Aside from hardware failures and software that you install, including OS upgrades, there is no reason that your computer should not work precisely the same as it did when it was new. 

Without a more specific description it is difficult to provide specific guidance. Read the following to determine if something may apply to your concern:

General Mac maintenance: Tips to keep your Mac in top form

OS X Mavericks: If your Mac runs slowly

The article is very cursory, but be sure to read through to the end. Unfortunately the "Repair a disk" link at the end points to nothing useful, so use this one: Disk Utility.

General purpose Mac troubleshooting guide: Isolating issues in Mac OS X

Creating a temporary account to isolate user-specific problems: Isolating an issue by using another user account

Memory limitations: Using Activity Monitor to read System Memory and determine how much RAM is being used

Identifying resource hogs and other tips: Runaway applications can shorten battery runtime, affect performance, and increase heat and fan activity

To identify potential hardware problems: Apple Hardware Test.

To resolve startup issues and perform disk maintenance, use Disk Utility.

Safe Mode or "Safe Boot" is a troubleshooting mode that bypasses all third party system extensions and loads only required system components. Read about it: Starting up in Safe Mode

To repair a potentially corrupt hard disk, so that you may recover its data prior to replacing it, and subsequently reinstall Mac OS X: OS X Recovery (applies only to Lion and later versions of OS X)

You've clearly upgraded from an early machine and I wonder if you had sufficient memory when you did so.

Here are a few hints from a respected member of the forums.   See how they may apply to you.

Tuning Mac OS X Performance