@ethan_gauld, unfortunately as apps keep getting bigger and updates increase the storage needed to keep them it's become apparent that 8 GB just doesn't cut it. Getting an SD card to put pictures and videos on helps, but the simple truth is that the main culprit is still your apps. So a few things you can do:
1) take stock of what's on your phone and regularly delete apps you no longer use.
2) apps also use quite a bit of cache storage. This is fairly easy to clear by going into settings>apps>all and clearing the cache on each app. This is tedious to do manually so I'd recommend a cache cleaner app that does all cache with one touch. Clearing cache doesn't delete your personal data, cache just helps you pick up where you left off in an app faster. Regularly clearing cache will also usually boost your performance a little bit.
3) clearing app data on apps that don't need it. In the same area where you find the cache for each app you can clear the app data. This will clear all saved accounts and information so you obviously want to be careful which apps you do this with. I sometimes do this with apps like Facebook or the browser that won't delete anything important. I have to sign into the Facebook app after doing this but that's no problem. And speaking of Facebook if you have it synced with your contacts that can eat up a lot of space too so you might want to unsync and clear the Facebook data.
4) Android 4.0+ has a freeze app feature built in that is great! Not so great is the fact that Verizon figured out how to block this for their own apps and won't let you freeze some of their apps. But you'd be surprised how much preloaded Verizon crapware you can freeze. You go to the same place as before; settings>apps>all, and pick the apps you want to freeze. Then uninstall any updates for that app, and then go back and choose the "disable" option at the top. Then this app will show up on the bottom of the list with "disabled" next to it. This won't remove the app, because it's built into the OS image shipped with your phone, but it will prevent that app from showing up in your app tray, and that app will no longer update and take up that little extra room.
That's pretty much the best you can do without getting more technical and trying to do things like root, install custom ROMs and such. There are some powerful apps that do cool stuff if you're rooted, but really that won't guarantee you'll never see the low space message when you still have limited room. Phone makers need to quite frankly just offer more room on their phones. 8 GB doesn't cut it anymore, especially when most apps are upwards of 30 MB. And really that 8 GB they sell you is closer to 4 because the OS and carrier apps take up the other 4 GB.
Sorry I don't have a solve all solution, that's part of the problem with current smartphones. But if you do some of the stuff above it should help. And smart, regular maintenance of your phone will help avoid the low space message. Part of that means getting to know your settings and stretching yourself beyond your comfort zone a little, which may eventually mean rooting your phone (like it did for me). But while rooting will help you, and allow you to use tools you otherwise couldn't, it's not the end all problem solver, and for some people it may be unappealing (it can be technical, and it may void your warranty if you have one).
Hope some of this helps though. These are the things that have helped me when I ran out of space.
