Ok, well, for me, what exercises I run depend on what I'm working on in my game.
For practicing ratting, I like levels 11 and 20 on insane -- I would try to do them with no deaths. The middle section of 20 is particularly good for punishing mistakes where you poke your nose out and aren't sure what's around the corner. Parts of 11 are like that too, particularly if the red hulks get loose. A single player exercise like that won't develop your mind game at all, but it at least lets you practice some tactics and -- maybe more importantly for me -- teaches caution.
For a while, I had trouble dodging homers without taking blast damage. I did runs on level 10 (start to blue key, no cloaks, no sniping), since there are a lot of homing missiles and a lot of walls. I like to think it helped, and it helped me understand what I was doing wrong. These days, I like Revodrav 8 / no invulns for looking at the same set of stuff. My homer fu is still weaker than I'd like.
When I first came back, Jeds watched one of my demos and told me my trichording wasn't efficient. He was right, I was hitting a lot of walls! I created to practice and sharpen all 8 directions. That came in handy. I don't always do a perfect triple chord, since it sacrifices a lot of visibility for a small speed gain, but the fact that I know *how* to and sometimes do it is, I think, part of why people think I'm fast. In the same vein, hosting up a level you normally play multiplayer and spend a while doing Stupid Kiln Tricks is a great way to learn timing and improve speed. I sometimes do that, too.
And this may amuse you. One of the big weaknesses in my game is taking stupid risks and being impatient. To help elimiate that . . . I play Nethack.
But I mean, this sort of stuff isn't necessary. I design stuff to help me get better at whatever I'm working on, but I don't always have a single player routine. Just if I think it's useful for something I'm studying right then. Some stuff is worth studying with a partner, too -- whether it's "how to dodge vulcan" or dogfighting or missile dodging or fusion or whatever. Bahamut and DK always seem to be game for drills, and some of the other guys seem pretty willing to train at something they're particularly interested in or good at, if you ask nicely.
Probably the most useful thing is demo analysis. Either watching my own demos critically, or watching other pilots' for ideas. I think that helps a ton to figure out what to work on, and then I devise practice routines or strategies from there.
But, that's my way of doing things. I am a student. That is the way I approach things. Plenty of pilots have gotten plenty better than me without doing any of that.