Well. Where to start. I truly believe that if one is in pursuit of true movie terribleness then you cannot limit yourself. The foremost and number one genre for this is horror. If you are looking for true horrible movies you MUST look at this genre. And do not fear for you will truly be rewarded.
Sheer horribleness you must watch the entire Return of the dead family. This is so awesomely great that my FIL and I watched about 6 movies back to back one day. To the sheer annoyance of SWMBO. Great day.
I have a four pack of British horror movies that are RIDICULOUS. I don't mean they are gorey, or scary, or even creepy. THEY ARE STUPIDLY AWSOME. The gem out of the bunch is probably this.
http://www.imdb.com/title/tt0084090/
I saw a few movies mentioned here that I take exception to. Cube for one. That is an awesome movie. The entire Saw franchise I believe is a rip off of these movies. That said if you want a crap movie don't watch that. Dog soldiers was also very good, considering the budget.
Another good horror flick that is horrible in a good way is.
http://www.imdb.com/title/tt0084090/
This movie is funny as hell. IMHO.
How about the Robocop series? That is pretty astoundingly terrible.
A couple movies by Matt and Trey are awesome in my opinion. I know you mentioned no gore so will give you some other options.
Orgasmo. Come on. The name alone is awesome.
Alferd Packer: The Musical
I watched Journey to the center of the earth, on a long flight a bit ago, that was torture. Not sure I would recommend that.
And honestly the best way to watch awesomely horrible movies is in fact MST3k.
I am sure I can come up with far better when I have my full wits.