I ran into it most recently in The Sea of Trolls by Nancy Farmer. *spoilers* Jack and Thorgil had made it to Mimir's Well and drawn the magic water and were returning home to save Jack's little sister. You'd think that after slaying dragons, surviving trolls, and convincing the Norse version of the Fates of their worthiness there wouldn't be any dangers left to face. Wrong. You can always throw in a few giant spiders to liven things up.
Now technically Mimir's Well wasn't the climax of the story. The climax was when Jack *spoilers* defeats the evil troll-queen Frith. But Mimir's Well was the climax of the Jotunheim section of the story because it was the hardest thing Jack and Thorgil had to do there. Readers weren't in too much suspense about whether Jack and Thorgil would escape from the spiders—of course they would. They'd already killed a dragon, for heaven's sake.
I'll probably visit The Sea of Trolls in a future post about when a character's death is lame, but I'll leave it for now and go to The Lord of the Rings.
This book has an anti-climax towards the end where the hobbits *spoilers* return to the Shire after Sauron is defeated and find it has been taken over by Saruman. This part isn't in the movies because only the most die-hard fans would stick around to watch it. Nobody doubts for a moment that after destroying an evil Maian dark lord the hobbits can't handle a little ol' wizard (whom they already defeated once at the height of his power). The “scouring of the Shire” has a thematic purpose, but it doesn't fit well into the story arc. Kill me if you like, but I'm quite glad it got booted out of the movie.
There's often an unexpected reappearance of the villain or a near death experience for the hero after the climax (what Blake Snyder calls a “moment of final suspense”) but cram in too many of these and readers start suspecting you of trying to boost your word count. One is good. Two is probably excessive.
The most notorious offenders are the post climaxes in which the defeated villain returns for his “revenge” (usually by attempting to murder the hero in front of his girlfriend or vice versa). After all, what villain's really going to bother doing that? A post climax shouldn't have the hero facing something he's already faced and overcome once. What's the point of making him face it again?
Build, build, build until the climax, give your readers one last shot of thrills and suspense, and then--you're done.