If no skill is set, and if I remember well, the game starts automatically with medium skill... I think it can give a good overview of the level difficulty ...
So if the player more fun / difficulty / death / blood / fights / gibs, he can restaart the game increasing skill setting... up to nightmare for madest players.. 8)) 

normal. I rarely even use other skills. 

unless it is a small map then I might try it on hard or nightmare. 

Easy.

(What? I suck at Q1SP dammit.) 

. 

I play on hard without playing normal first because SPQ1 on hard isn't unbearably hard for me.

With the exception of Q2, I play all other games on normal except for any MOHAA add-on in which I play easy.

As a trend, I find that most newer games are a lot harder on Normal then older games were on Normal. 

I also like to play on hard. But lately I was playing Bastion on easy and it was lot of fun (I think it's due to the changed skill rules on this map - weaker monsters instead of reduced monster count). I decided to play on easy because I wanted to finish the map on first try and was afraid of the number of enemies.
As I was reading the thread about this map I noticed that nobody is telling on what skill he was playing. Maybe Necros, Shambler, Underwoldfan and others don't even mention it and start playing on Nightmare... 

which I think is the most difficult for the mapper, since it should be balanced to be a challenge, but never frustrating.

Easy can always be a walkover and hard+ can be ridiculous, but Normal should tread a fine balance.

A good, recent example is the Bastion map that at first appeared to have overly difficult end combat when I first made a god/quad test-run to see how the engine managed the load.

Then when playing properly on Normal, it was most enjoyable. Definitely challenging, but not frustrating.

I believe that it's also essential to keep in mind that the player doesn't have to use all weapons or powerups just beacuse they're there. Just ignore them if you feel you can do without them and leave them for those who need it. 

For Quake:

"All levels are played on Hard skill, where applicable. "

I play on skill 2 because I always have, well for the last 5-6 years anyway. It allows me to get a proper feel for a map in comparison to others, and seems to provide the optimum challenge.

For other games (since they do exist...):

Quake 2 - Hard
Unreal - Medium
Almost all FPSs - Medium
Most 3PSs - Medium
Esoteric 3PS / other sorts of game e.g. RTS - often Easy