HUD in general or only Compass? With no HUD at all I don't know how much Health I have and I prefer knowing those things before jumping off cliffs and such.
But no Compass is amazing, I really like to play like that.
I wish I had that option. I am on console, so the only way to loose the bleeping compass is to go no HUD. You have to guess at your health, but with some practice you can get fairly accurate at it and you can always check the skills screen if you really need to know. The annoying thing is that you miss out on all messages from the game, and I like to know what reward I just got for completing a quest, was it gold, was it an item (and if so what). With no HUD there is no easy way to tell what the reward is since my inventory is so large that searching through it to see if I got something new is a pain.
If I had the option to go no compass and no sneak crosshair, I would take it, but being on console, I have to settle for no HUD.
Re: the OP, yes it is amazing. Really makes you feel like you are exploring when there are no compass icons and those bleeping red dots giving away enemies locations are just no fun. Crosshair/sneak crosshair makes aiming too easy and distracts from immersion. No sneak crosshair also means you have to really pay attention to your surroundings to determine whether you are hidden. Much more immersive than staring at an "eye" in the middle of your screen.
EDIT: I do turn the HUD on in my house if I want to read books in my liabrary. Otherwise it is a real pain to select a single volume from yoru shelf since you cannot read the spines without the HUD.
I also turn the music down to the lowest notch before the music becomes inaudible. I would turn it off completely for increased immersion (and sometimes I do) but it is beautiful music and I usueally like hearing it in the background.
I play on expert mostly. I don't have that good of hand eye coordination or twitch skills, but playing this way forces me to pay more attention to terrain and battle strategy (like with bears, shield bash then flank) instead of trying to approach every opponent head on. Its more fun, at least for me, to have to "think" about battles. Sometimes if I am tired or just in the mood to kill stuff without having to strategize battles, I will bump it down to Adept.