Some of these probably have already been suggested, but I don't really want to wade through 33 pages to find out.
Sounds fine in my head
Angel of Memory:
Simple. The screen does not display anything outside your immediate view. When you wander into the next room, the area you've walked through doesn't become dim, it goes black entirely. If you can't see it from where you stand, it's not displayed at all. Computer maps make walls and whatnot display, but wouldn't display items or the stairs. Find them yourself.
Angel of Iron:
Instead of having your pick of traits, your MaxHP rises as if you had taken Ironman when you level up. Your maximal HP will skyrocket, but you have to learn how to use weapons effectively without so much as Eagle Eye to cover their weaknesses.
Angel of Chance:
Level exits only spawn after flipping a switch. Every non-special level has at least one, obviously. Levels with more than one basically force you to prepare for the worst. Switches should probably be spawned more often to go with it; if there's only one switch on the level, it's obviously the one you want. Early on this wouldn't be too bad, but later in the game the fact that you have to find the right switch, survive any wrong switches, AND find the level exit afterward means it'll be very hard to do controlled dives near the endgame.
Blocks Gambler's Shield, obviously. And should probably not spawn nigh-gamestopper switches (like the "everywhere is lava!" thing) though that might be balanced out by also removing the "kill all badguys" switches too. Homing Phase would need to change behavior (Or just not spawn); it could teleport one to the exit switch if the exit isn't already spawned, or maybe it just acts as a regular phase device if the exit isn't around.
Probably retarded:
Angel of Vile:
You have Arch-Vile powers. Alt-firing with empty hands (No weapon selected) lets you use the Archvile's magical fireblast of doom. The problem is that anything killed with fireblasts results in destroyed loot. Also, corpses in your view randomly respawn.
Angel of the Warp:
Changing tactics does not cause you to run, but instead acts as a phase device and tires you out. In your former place, a random demon is spawned (Not a former human). Phase devices used by anyone have the same effect; a former human using a phase device will warp across the map, and a Hell Knight or something worse will arrive where it left from. And for whatever reason, an inordinate number of monsters are carrying phase devices. Phase out of a bad situation if you need, but beware the Mancubus that spawned in your place.
Angel of Hell:
You are a Hell Knight; you cannot use regular weaponry, but you have a built-in plasma launcher and a mean right hook. No traits, but at level 6 you mature into a Baron of Hell (Armor/Health upgrades, improved natural weapons). Demonstrate that you are the baddest monster in Hell by destroying the Cyberdemon yourself.
Lack of weapons are made up for by the natural weaponry they have, though it lacks a certain punch later and can't be modded. Armor works as normal, on top of their natural armor. Probably should have limited inventory (Where you gonna carry that crap? Your naked hide?). The early game will be a slaughterfest as you mow through Former Humans, but later monsters won't take your shit and you don't have the firepower or special traits to force the issue; that plasma/acid cannon isn't anywhere near as effective as a rocket, to say nothing of a BFG.
Would probably be an awfully gimmicky thing, though.