Other than the obvious Record of Lodoss War (both OVA and TV versions), I will echo the support for Slayers (hilarious), Scrapped Princess (fun), Escaflowne (mecha), and Berserk (dark).
I especially reccomend the Berserk manga, rather than the anime. The anime ends before the story even gets going, so you will need to go to the manga eventually, so just start reading it sooner rather than later.
It is a bit gothic, but Vampire Hunter D, especially Vampire Hunter D Bloodlust, somewhat fits under the definition, and is fairly good.
The Twelve Kingdoms is based more on Chinese and Japanese aesthetics, but it is a great fantasy story filled with monster-slaying and politics. One of my favorites.
The .hack stuff kinda counts, except for the being inside a videogame part.
I know there are a lot more, but I can't think of them...
Err... I never watched it myself (can't find the budget), but Aura Battler Dunbine is a mecha series that takes place in a land of fairy tales. Older series, but well-regarded.