MDl should really put up a page of all these websites and their ratings
DramaFire/ MyAsianTv / Kshowonline(Variety) /DramaCool / and gooddrama
For watching on the TV (via Roku) I use mainly DramaFever, and occasionally Hulu, Netflix, and Viki.

For watching/downloading online (with hard subs), I like MyAsianTV and KissAsian.  I used to use DramaCool, only because they had a large selection, but I was never very happy with the quality of their vids.  I just recently found KissAsian, and they have a huge selection with much better quality vids.  They're my new go-to site, and if I can't find what I'm looking for there, then I check MyAsianTV.

For good quality vids with soft subs I used to use Doramax264, but I haven't been able to pull up the site for the past few days.  I don't know if they're just having server problems, or if they're gone for good...
gooddrama.net
dramanice.tv
dramacool.tv
dailymotion and youtube occasionally
Doramax264
myasiantv.se
dramafire.com
drama.net

I am having a very difficult time finding websites or mobile apps (Android) that have a good selection of Japanese dramas, the classics as well as modern, historical, etc., any suggestions?

I prefer to download directly from the fansub or d adcits, streaming sites sometimes steal the subs and win money with it  

(I olnly watch jdramas)

literally at home after finishing every imp task 

sources which mentioned above in comments

I use Kissasian:

http://kissasian.ch/

 Hotsushi-kun:

I use Kissasian:

http://kissasian.ch/

I use that too but recently its been lagging and now there are porn ads X-l

Kissasian has the best selection I've found, and usually in hd, which is important to me.  Though, the site does drive me crazy sometimes, it's tolerable.  One of the dramas I'm watching right now seems to only be available with eng subs on here.

Otherwise, I watch stuff on Dramanice, Fast Drama, Putlocker, Netflix, and Newasian.  I gave up on dramafever long ago, they let me down, and Hulu's selection sucks. 

 ShotaSidePart:

I use that too but recently its been lagging and now there are porn ads X-l

At the very moment for me, the porn ads are gone (within the last couple days).  I don't even care about getting sidebar ads, but the porn ones are really not okay.  And the porn pop ups... D:  Every time I click anywhere, I have to be ready to close one.  It does get annoying.  

So, use Kissasian with caution!!  I wouldn't use it at work.  haha

those are the best i found 

123movies little ads

yesmovies  little ads

yifymovies  little ads

putlocker No ads

hdflix  little ads

APPS - viki, tubi tv, asian crush 

Online - KissAsian, KissTVShow, Youtube