Serial Experiments Lain, NHK ni Youkoso! Recommendations
Both contain extensive and exhaustive commentary on a particular modern social phenomenon: in Lain's case, it is on internet personae and the nature of the online world itself, while NHK explores the world of Otaku and anime fandom, as well as those with crippling internet addictions, "hikkomori", and other people whose daily existence is hampered by paranoia.
NHK, although still difficult to watch at times, has the greater level of "entertainment value", although neither is exactly "light viewing" and both contain some very disturbing parts. Tone-wise, NHK is noticeably more humorous and dialogue-heavy, while Lain is the more self-consciously "abstract" of the two.
Hikkikomori lifestyle, internet culture, paranoia, and possible hallucinations.
At its heart, welcome to the NHK is a show about isolation and loneliness- the symptoms of being a hikikimori. I'm glad to see that everyone else has recommended other well known shows that have a main character with a screw loose, and I certainly recommend those on their own. However, I think that another series you might consider picking up if you want something more similar to the darker parts of this show is serial experiments lain. It's complicated and hard to understand, but I think that welcome to the NHK is good a place as any to start.