Every single band that I think is horrible excels at sucking in some particular way... and usually is so good at that particular way of sucking that I can't really call them horrible. Nickelback is for example a very successful band. They sell out shows and know how to play instruments. Their vocalst can even sing. These qualifications are already well beyond "the worst". And then on top of that there's the fact that they've created a cookie cutter method of creating generic & bland rock-like lullabies that appeal to a large segment of the population. These guys are succeeding big time while also sucking big time. At the same time. That's not easy to do.
I think to be in the worst band, you can't really be financially successful on such a scale, some of your band members can't know how to play instruments, and you have to suck at a lot more than just writing good songs and performing them.
I used to go to a lot of punk shows when I was in highschool, and most of the time it was random local bands. You pay $5, you see 6 bands, you get a good workout in the moshpit for a couple hours, and go home with your ears ringing.. And some of those bands were absolutely horrible. They just sucked at everything. Oh, there were a lot of good bands too! It's just that there were some really bad ones in the mix. It just came with the territory. A lot of good bands, but when they got bad, the standards were very low, so anything was possible. And some of them might have just been kids or part timers, but there were actual "this is my full time job, i drive from town to town and play punk rock wherever I go" type dudes..
So I've definitely at some point seen a couple bands that might qualify for a "the worst band ever" type label.. but I couldn't really tell you which bands that might have been. So let's go with the black eyed peas? They look rock enough to me.