I once challenged myself to build the simplest, epic-viable build I could do w/out heavy spellcasting. It was almost entirely Paladin: Battle Blessing + Ride-By Attack + Find the Gap + Power Attack ... and that was mostly it. I think it also acquired really good reach (30 feet or thereabouts) and had Stand Still and the Steadfast Boots.
Paladin w/ an epic charisma covers most of your saves, and you could mix in Hexblade or various other matters to taste. Sure, you'll fail every so often, but get a few items that give you a re-roll once per day, and that should usually take care of it. Unless the enemy has pounce, you're only subject to 1 attack, and you can get quite a good AC (at least as good as any PC can get) and typically Stand Still will stymie them in melee combat anyway. You've got only 1 attack, but it's a good one, below ubercharger damage but still high enough to be credible.
The build worked for the session or two that I remember us playing w/ it. And, that's not counting stuff like Devotion feats (I don't think they existed at the time). Crucially, though, it's assuming enemies that are essentially from the books -- i.e., the opponents aren't really optimized. It's also heavily gear dependent, Freedom of Movement being a necessity, but that's hardly unique: all D&D characters are, and epic ones just moreso.
