Just my personal favorites, not all of them are amazing and this list certainly isn't meant to be a 'greatest anime of all time list.'
It's more a 'if you were locked in a room and could only...
It doesn't necessairly mean "the best", just the ones that touched the right strings with me, or that I have the fondest memories of.
Lain isn't really Drama, I just like it a lot :X
Numbers are order I would watch them in.
(Full Moon wo Sagashite is the missing #12 on the list; for some reason, I haven't been able to put it on here.)