I find that using SMSBackup+ to backup all of my texts/call-log about once a week (500-1000 backed-up items per week) and deleting them, after running the Personalization for Swiftkey3, helps. Having 20 different text threads open with 200-500 messages each really adds up! Plus, it sends them to you via an email to your Gmail account, so you will have every text/call ever sent/made!
Another is to make sure that you clear your cache regularly enough for "cache-hungry" apps: Browser, Gmail, Yahoo!Mail, Play Store, etc. I do this probably once every day or two, and it clears ~35-70MB of data each time. If I go a week, it's well into the hundreds of MB's (I use my phone a lot).
Try downloading ROM Toolbox, an EXCELLENT app and one that I now cannot live without. I am not sure which features work without root, or if any, but it's worth rooting your phone just for this app! You can manage your apps MUCH more carefully/closely than with just the Android Settings - Apps menu, and even run any operation in batch mode to save time.
Under "Settings - Apps - Running Apps" go ahead and force-close anything you don't need, so long as you know what it is.
Disable any apps (i.e. system apps) that you don't use, so long as you know what they are... This would be things like Books, Movies, Voice Search, etc.
DISABLE "DRM CONTENT PROTECTED STORAGE"
Make sure your camera isn't constantly running in the background!
And remember to reboot your phone 2-3x/week. It only takes a minute, and it is the easiest, quickest way to fix any ills your phone may be suffering.
*Note: If you have a lot of browser tabs open, and don't want to lose them all when you reboot, make sure that you don't clear the cache and them reboot immediately after (you have to go in and reload each tab); also, don't reboot and them immediately clear Browser Cache, instead open the Browser (which will restore the previous tabs) and once everything is loaded, then clear cache. I hope this saves you some headaches, it took me a few angry mistakes before figuring out that I am, indeed, an idiot haha.