The whole myth comes from a misunderstanding of how and why mobile operating systems use RAM – usually, users make an analog between that and the RAM on a Windows-powered PC, where we've been taught for decades that more free RAM is always better. See, there's a difference between how PCs handle RAM and how mobile devices do, and these differences come from the developers' own idea of how the respective device should work.
How a Windows PC treats RAM
So, here's just the condensed basics, to help anyone who's hazy on the subject understand this argument better. RAM (random-access memory) can be viewed as a blazing fast temporary storage unit, which was introduced in computers back in the day, in order to help them keep currently running programs' resources easily accessible, rather than having to re-load them for every action the user takes. For example, if you open up a browser and add its first tab, this first process will be a bit slower. However, once booted, it will load the resources needed for new tab creation in the RAM and your second tab will open almost instantly. Furthermore, now that your browser is in the RAM, the PC's processor and hard drive have a lot of load taken off their back and you can freely open other programs, while the browser is still fully functional – either in a window, or minimized.
Sounds slow and tedious, doesn't it? Well, that's why users try to keep their PCs' RAM high and unwanted usage to a minimum, killing unneeded processes, and keeping a keen eye on rogues. Ultimately, Windows will attempt to keep everything on your PC running, even if it slows it down to a halt, which is the reason why "close unused programs" is a PC user's mantra.
Android keeps RAM full by design
thinks you will want to glance at in its memory. So, if you set up your email app, Facebook + Facebook Messenger, Vine, Twitter, Viber, WhatsApp, Hangouts, Evernote, etc., try as you might to terminate them – you will not be able to. Sure, you may close the apps themselves, which will unload resources from the memory and cache, but you should not attempt to close, nor be bothered by, the ever-running processes behind these apps. By design, they can't, and shouldn't, be killed, unless you just uninstall them.
As far as resource management goes – you leave this to Android. As previously mentioned, Google's OS will fill up about 80 - 90% of your memory with whatever it deems worthy. However, if it happens to need memory (for example – the user launches a large game), Android will terminate the lowest priority processes without mercy – it does not matter whether an app is responding or not, it will go "bye bye" instantly, with its state nicely tucked away in a temp file, so the next time the user opens it, the app will (or at least – should) open in the same state it was when last viewed.
Android doesn't do swap files, it doesn't try to keep everything running, because it has limited space to work with, and because slowing down user experience on a smartphone is a big no-no. Therefore, a process on an Android-powered phone has two states – "running" or "sent to oblivion".
Now, there is the case of the random rogue app, which uses up resources for no apparent reason, and let's say you are put in a situation, where you don't have the option to delete said app (because of reasons) – killing the app might not help, as it may start itself up again at any random moment. You can try hibernating it with a tool like Greenify, which will disallow Android to open it at will.
So, how do I optimize my phone?
Are you a tidy-as-Virgo RAM-cleaner? Try going for a week without the “optimization” apps, see how that affects your phone.