There are normally two causes of severe slowdown.
1. Low free memory - you can try uninstalling seldom used apps, clearing cache, etc.
2. File system fragmentation due to repeated installation/removal of apps over a period of time. If you are running Jelly Bean 4.3 or later, the built-in TRIM support will take care of this for you. Otherwise, a factory reset is the only real solution. Be sure to back up whatever you can first before doing a reset, as it will be gone afterwards. Any apps obtained from the Google Play store will already be backed up (but not their data - e.g., game progress, personalizations).