Battle beyond the stars. Not very well known self-aware star wars rip off with some humor and pretty good scenery for the budget and the time with George Peppard as “Space Cowboy” - yes, really. It’s fun!
You may also like: Gremlins, Critters and Tremors, for cheesy sci-fi/action 80s stuff.
One of the greatest movies of our time, nay, all time, as measured in pure unadulterated zaniness.
THE greatest movie is, of course, Demolition Man. Which has a certain SF element to it (defrosted Sylvester Stallone in an incredibly ridiculous future) but no rocket ships going boom.
Um, yeah, and I just re-read the OP and you’ve seen Ladyhawke. D- on reading comprehension for me. 
Just don’t watch “Reign of Fire.” That movie actually made me stupider.
Oh, and Zardoz. It’s got loads of boobs and Connery in the most ridiculous outfit ever.
Not sure if the ending is a happy one, though - it’s sort of hard to tell.
ETA: Demolition man definitely counts. As does Judge Dread.
Oh, and Planet Terror
If you can find it, trySix-String Samurai
In the fantasy genre, you can’t go past The 13th Warrior, It’s a bit dark and gritty, and the ending is… satisfying more than happy. But great Sword (and not so much sorcery) fantasy.
If you haven’t come across the new Sparticus TV series yet, it’s also some pretty good Sword and Sandal action. Again though, not so good on the happy ending front.
Or Kull the Conquerer, a very cheesy Sword and Sorcery flick starring Kevin Sorbo (of TV series Hercules fame).
Note the OP.
Another vote for Krull—good, big-damn-fantasy movie. It apparently was actually supposed to be the first Dungeons & Dragons movie, but they lost the license before release. Nice cast, great music.
On that note, do not watch the official Dungeons and Dragons movie. I mean, you can, but you’ll probably regret it.
I also agree with The 13th Warrior—a criminally underexposed movie. Though as a matter of fact, I never really thought of it as a “fantasy” movie till now, more just a plain “adventure” movie, though I can see how it could qualify. But now that I think about it, I think when you get down to it, it might actually be closer to “historical science fiction”!
As for sci-fi…I’d go with Tron, if you can find it. I’m actually puzzling a bit over more-than-decent sci-fi movies with unambiguously happy endings…The Fifth Element works, I’d say. Of course, as Ray Bradbury put it, technically, Singing in the Rain is a science fiction movie. And a musical, too!
I was going to recommend The Last Starfighter, but now I’ll recommend Remo Williams: The Adventure Begins. It’s more of a martial-arts/action movie than a fantasy, but it has feel-good fantasy elements to it as well.
And an awesome soundtrack. Listen to this!
Street Fighter. Long live the Pax Bisonica!
Mom and Dad Save the World
Epic adventure to happy ending… I hope I didn’t spoil it for you! 
I gotta watch something with a title like that.
And thanks, everyone, for the suggestions! I added lots of interesting titles to my watching queue.
Allow me to expand the target a bit then, to include animation, both for adults and kids (Coraline was really quite good!), and both Western and Japanese. Series are also OK, provided they’re not too long - a friend lent me Trigun and Outlaw Star, and I’m having great fun watching them! Especially Outlaw Star, I got to run a role playing campaign based on that some time.
Iron Giant is inarguably one of the best animated films ever made.
And I also love Disney’s Tarzan.
Meet the Robinsons is a fun romp, too.
And another. Watch out for Liam Neeson in a minor role.
Note that the film (and the book it’s based on, “Eaters of the Dead”) is basically an unsubtle adaptation of Beowulf told from a third-party perspective. Hell, the Beowulf character is named “Buliwyf”, the monster is “Wendol” (Grendel), and so forth. That said, I enjoyed it. Worth a watch.
This isn’t fantasy, sci-fi, or animated, but when I’m feeling down, my favorite movie to watch is The Best of Times, with Kurt Russell and Robin Williams.
I know a group of people who get together and watch it every New Year’s Eve.
Outlander is a sci-fi movie based on Beowulf. Jim “Jesus” Caviezel plays a soldier from another world who follows an alien monster to Norway in the Viking era. The cast is pretty good, including Caviezel, John Hurt, Ron Perlman, and Sophia Myles. The monster itself is pretty cool, too.
It does. And it has Barbi Benton in it, and they were smart enough to not let her speak.
And try Deathstalker 2. It is hilarious. And has a happy ending. One of the road signs points to Fredonia, the heroine is a princess who can tell the future who doesn’t understand why telling a king that he is being cuckolded doesn’t go over well, and in an early bar scene the words “hello, sailor” is used in context.
Real Genius, mentioned above, is a great movie but not really science fiction or fantasy.
I never saw it, but it led to my all-time favorite title for a review: a gaming site declared, “Dungeons and Dragons Movie Fails Saving Throw Against Sucking Ass.”
Highlander but NOT THE SEQUELS
Second the recommends for Stardust and the Flash Gordon movie.
Second the warning about Dungeons and Dragons which goes right through “so bad it’s good” territory and comes out bad again.
It’s not fantasy, but Rob Roy has most of the trappings and an all-time great swordfight.
There are better fantasy movies but Eragon is worth a look.