Q: imac

Check the integrity of your hard drive

Resolve startup issues and perform disk maintenance with Disk Utility and fsck - Apple Support

if nothing is found proceed with this test as outline in the article.

Using Apple Hardware Test - Apple Support

See this as well, it could be another cause to the symptoms your seeing.

Resetting the System Management Controller (SMC) on your Mac - Apple Support

Any fresh reinstall is never a bad idea provided you have the necessary installers and a backup of your current setup.

Before you do try that what were the results of the three tasks I posted?

Also remove any and all USB devices from the computer (except the keyboard and mouse)

is there excessive heat or cold where the computer is kept? Is it in a well ventilated area? Is there pet dander or hair around the intake ports?

Backup, backup, backup if at all possible to protect your data.

If you can get EtreCheck downloaded and run, it would be useful to see the output

<https://discussions.apple.com/docs/DOC-6174>

Look at Applications -> Utilities -> Activity Monitor to see if there are any processes that are hogging the CPU.

Look in the Applications -> Utilities -> Console logs to see if there are frequently repeating log entries that may indicate a process starting, failing, starting, failing, starting, failing, wash, rinse, repeat.  This kind of activity would not show up in Activity Monitor.

If your data is safely backed up, you can try a clean install.  Or if you can partition your disk to give yourself a 20 to 50GB partition, install a clean OS X into that and see if it works OK there.  Of you you have an external disk you can erase, install a clean OS X on that (it will by definition run slower because it is running over USB, but some behaviors are not going to be affected by the disk speed).

Activity Monitor - Mavericks  also Yosemite

Activity Monitor in Mavericks has significant changes

Performance Guide

Why is my computer slow

Why your Mac runs slower than it should

Slow Mac After Mavericks

Things you can do to resolve slowdowns  see post by Kappy

6 Easy Tips to Speed Up OS X Yosemite on Your Mac

If this started happening without your having made any changes and without a warning of low disk space, then it's likely that the startup drive, or some other hardware component, is failing. Back up all data immediately, then make a "Genius" appointment at an Apple Store to have the machine tested.

There are ways to back up a computer that isn't fully functional. Ask if you need guidance.