Is an external battery for a smartphone a good idea?

That depends. It depends on what phone you have, how often you're able to charge it, and how well you choose to manually regulate the battery-draining aspects of your phone. For me (I have a Galaxy S5) it's not necessary because I charge my phone every night, and when that's not possible (during camping or something) I have power-saving and ultra-power-saving modes, plus an app called Juice Defender that keeps background data flow minimal, and I try to keep my wallpaper and all reading apps etc to a dark theme. It really extends battery life, and I haven't run out yet.

As for Spec99's info, it used to be true, but not anymore. Phones used to use nickel batteries, and it was better to let them die and not leave them plugged in any longer than necessary, or the battery would stop holding a charge after a while. Now, all smartphones (that I know of) have lithium-ion batteries, and software in place to keep any "overcharging" problems from occurring. I've heard most often that you should always try to keep your lithium-battery phone above 30%. Here's an article all about it, and the article actually suggests keeping it above 50%:

http://gizmodo.com/how-to-take-care-of-your-smartp...

There is a science to charging a battery. If you constantly charge it even if it is not dead it will decrease in charge faster. It is always better for a battery to fully run out of charge before charging it to help save battery life. (You will see construction workers holding the trigger of a drill to let the battery fully run out before switching batteries for this very reason) I have an external battery for my phone and I do not use it very often as I always charge my phone at night. However, the times that I have run out of charge and was able to connect the extra battery it was a lifesaver especially in places where there is limited access to power like the woods or a restaurant. I would recommend having one as a backup but I never used mine enough to even consider if I would lose battery life in it.