I've read that its best unplug after it's done charging. I guess it can effect the battery over time. I would say that if you are able to unplug it right away then why not? Unless you are expecting to be away from a charger for a long time and want to have as much batter as possible then thats your choice. I usually leave mine plugged in while i'm sleeping so obviously I can't unplug it until I wake up. I don't use battery doctor though so I can't comment on that.
When the battery is fully charged, the charging circuit in the phone stops charging the battery. If you leave it on the charger for a few days, it's going to drop a little charge (even if the phone is off) and when it drops enough the charging will turn on again and top the battery off - so when you finally unplug it, the battery will still be fully charged.
You should always leave the charger on for about 30 minutes after it reaches full charge anyway. The way state of charge is measured gives you a 100% indication at about 98% charge (which is why, if you unplug the charger the moment it indicates 100%, it will usually drop to 98% almost immediately).
I've left phones on chargers for months at a time (sometimes, in a busy shop, you plug in a phone under your desk or somewhere else you don't often look - then forget about it) with no ill effects.
About the only risk - and that's whether the battery is charged or not - is that the charger can decide to go bad any time, and start a fire. The longer it's plugged into the wall, the greater the odds, but we're still talking about fewer than 1 charger per day doing that in the entire world - much less than 1 per day. Your TV, toaster, refrigerator, lights - everything powered by electricity - carries that risk. And you don't unwire the lights in the ceiling when you're not using them, but fluorescent ballasts go bad more often than phone chargers do.
What rukbat said. I'm sure the majority of us go to sleep with our phones plugged in, right there at the night stand, overnight. I've had my S5 for almost two years now and have charged it this way everyday. No battery problems here.
What I do suggest is that you get rid of that Battery Doctor app. I had it installed for almost a year on my phone and honestly, it doesn't do you any good - probably sucks more juice than anything.
I've had my Note 3 since October 2014 and am still running on the stock battery. (My wife got hers at the same time and is also still on the original battery.)
I've had my Motorola V551 since it was released (summer of 1004) and the original battery is still good.
I just never let a battery drop below 40%.
(Unfortunately, NiCd batteries don't last that long. My MicroTACs won't keep enough charge to run more than about 115 minutes. But they're about 25 years old and there are no more analog towers for them to connect to anyway.)