I see this topic's quickly devolved into "anime I don't like" and "popular shows that aren't as good as their popularity would indicate" (yeah I agree guys allot of it is bad but the question is for bottom of the barrel). I'm gonna take an actual shot at answering the question. Let me just preface my response with that 10 years ago I watched allot of anime. As in, huge stacks of DVDs I would consume in weeks and subs I would tear through at lightning pace. Of everything I watched, by far the worst and trashiest is the 2004 TV series DearS.
DearS hits a bunch of the notes. Hapless teenage boy who lives by himself inadvertently enters a master-slave relationship with a hot, scantily-dressed, mentally challenged alien chick who he tries to "civilize" to humanity to whacky results because - surprise - their race's culture is based on master-slave relationships. He does have help though: The competent but decidedly less hot daughter of the landlord who puts up with all this because they're childhood friends and it's revealed near the end (concretely!) that she likes him!
The first alien chick apparently wasn't supposed to show up though, and a second hot alien chick (who also happens to be a tsundere) moves in to teach the first one how to be a proper slave, much to our hero's chagrin who just wants to do the noble thing of course and treat her like a human. They all also go to school too where everyone naturally fawns over the hot aliens and nobody gets much learning done because their one teacher is a total nympho who comes to school in lingerie and turns situations that didn't already have sexual misunderstandings into just those.
There's also a bizarre subplot with an alien catgirl (emphasis on the 'cat' part in her behavior) on some kind of mission that's awkwardly shoehorned in and breaks the flow of any episode she appears in because her relation to the main plot isn't adequately explained for... the entire run? I think she ties in to the last episode to help close out a show that's obviously about nothing else except fanservice.
Also, the show looks bad. I don't have a good eye for good or bad art and animation unless they're far on one side of the scale or another. This one's definitely on the bad end.
DearS earns bonus points for super generic openers and closers for that era. I'm pretty sure it's a copycat, probably trying to cash in on Chobits' success. Anyway, the ender has chibified versions of the female aliens doing a little dance to an upbeat track, pretty standard for that type of the show of the time. The opening is super of-that-era and totally shameless, even for the era. A second, high-pitched vocal support timed with the rising background music in a way that's supposed to sound sexual (the image on-screen includes the female lead falling in water towards the other alien chick to a forbidden lesbian kiss, while perioidcally cutting to bubbles containing images of her nude, upper body). Perioidcally there are shots in the opening showing the aliens moving in to the camera as if to kiss the viewer. And the part that gets me the most that I don't think I'll ever forget: The lyrics when the lead alien chick moves in to kiss you are "I'M YOUR SLAVE!" The rest of the opening is just super-generic and totally of the era: Shots of the supporting cast doing their 'thing', a pan of the whole supporting cast staring at the camera (as if to establish some sort of credibility with the audience that this show will be about something other than just whacking off), action sequences distributed in no particular order, a pan of a mysterious, comatose chick in a tube or something I guess. It's got allot of elements of '90s openings but with all the fanservice of the '00s, and this one's dialed up to 10.
... DearS is more bad than anything else though. It's not even bad-good. It's just bad. I could probably find something more generic but it would also be better. DearS is just awful.