1 I'm tempted to say, "Angelic Layer, because they didn't do one and I really wanted them to!" But that would be cheating.   I haven't actually seen all that many "extra" episodes; they're not all that common. The worst ones I've seen were the two for .Hack/Sign, but only because they were as mediocre as the rest of the series was.   Would you let me nominate the first "Key the Metal Idol" movie? It was 90 minutes which consisted of nothing except backstory exposition.

2 OK, I looked it up and Fushigi Yuugi Eikoden is a 4-episode OVA sequel. Now that I understand the rules of the game, I definitely have a nomination: the second El Hazard OVA. The story was completely derivative, Princess Fatora was intolerable, and the appearance of the second Ifurita made no sense and ruined the ending of the first OVA, which is the only El Hazard story that's actually worth watching. (What? Were the ancients turning out doomsday weapons on an assembly line or something?)

3 Yes, that's a bad one.  Right in line with Eikoden, it smushes one of the most important points of the original story.

4 The third Fushigi Yuugi is pretty hard to top. Heck, the only worthwhile thing about the Fushigi Yuugi OAVs was that series of shorts after each episode of the... second OAV, I think. I suppose Evangelion: Death & Rebirth deserves a mention too... hmm. I'll have to think harder on this.

5 I nominate the entire Invid arc from Robotech.

(yes, I'm reaching here.. I'm a fledgling, remember?)

6 I think I'd have to nominate the Rahxephon movie on pure waste-of-money factor. Spend two hours rehashing the plot from the series without all that pesky extended cast and character development.

7 Some nominations:

Evangelion: Death. A movie, rather than a bonus episode... but it was a movie that consisted entirely of recaps. It was double-billed with Rebirth... but that itself was included in End of Evangelion. So basically, the whole Death/Rebirth movie was redundant.

Pilot Candiate/Candidate for Goddes - The whole series is told entirely in exposition. So's the movie.

The Onegai Twins OVA tends to mess up the ending of the series, so let's mention that as well. Hopefully, one of these qualifies.

8 At the risk of offending our host, I'd probably have to go with some of the Tenchi spin-offs / movies / etc. but I can't decide which ones.  It's not that they're especially bad compared to some of the anime out there, just they're a significant drop from the original series.  It's especially hard to explain given the jumps in continuity between the various series, and trying to determine which are bonus features and which deserve to be treated as seperate works.

The original OAV series is better than the first TV series.  The first movie (Tenchi Muyo in love) is one of my all time favorites, but its a derivative of the first TV universe.  Anything with Sammy / Pixy Misa is a guilty pleasure and yet another spin-off universe.  The other subsequent TV series range from so-so to pretty lousy.  The second movie is pretty bad, and the third is merely ok.

My personal favorite bonus episode is the 14th episode of Dual.  Although it completely destroys the premises of the final episode of the regular series, it throws a very odd yet amusing spin on the whole affair.

9 The Tenchi spinoffs range from unncessary (Universe) to outright sucky (Tenchi in Tokyo).

Except for the Pretty Sammy TV series, which rocks.  Because it has Pixy Misa in it.  (And because it's a good story, well told.)  The Pretty Sammy OVAs aren't that great, though I like the second one, which is an unashamed assault on Microsoft for operating-system bloat.