Lots of great info here. Things I look for:
Proportions and design - whether a new pattern or a take on an old pattern, how does everything look. Is the handle a pleasing shape with nice lines, same for the blade, and then do they go together well and look appropriate both open and closed.
Fit and finish - Custom knives should have a much higher level of fit and finish than production knives. My ideal is for a tight fit between liners and backspring, centered blade, zero blade play, flush spring in all positions, pull just right for the type of knife it is (a small pen knife can have a 4, a backpocket I'd like to see at a 7 and everything else somewhere in between depending upon what it's intended use is). Now...and I think this is important, one must remember these are handmade knives and perfection is rarely if ever achieved if you're willing to look close enough. This was a lesson that took me a while to learn but I think it's an important one. I picked up a custom knife recently that had a slightly off center blade, the maker even told me himself when I started looking at it. Didn't take away from the fact that I love the design and the overall quality was incredibly high. I decided that, as a complete package the knife was excellent and was something I wanted even with the blade being slightly off center. I've also seen other knives from some of the biggest names in the game with blades a touch off center, blade play, tiny gaps in the back spring to liner fit if you hold them up to the light, etc. These guys give it their and what they are able to produce blows me away, but don't forget this is one guy in a small shop with a small room full of tools and machines able to create what is essentially usable art. Don't lose sight of that fact over some small perceived flaw in construction. I know Tony Bose has said something to this effect before, something about makers not becoming something when they enter the shop....I tried to find the quote but couldn't, so if someone knows it off hand please post it...it is one of the things that helped me look at things properly.
Style - do I like the pattern and the way the visual treatment was executed. I like a variety of knives but not all. I'm not huge on filework, I appreciate the skill but it's not likely something I will want on a knife for myself. I don't love MOP as a handle either. I do love stag, good bone, and even micarta or wood. I like bolsters and I like shadows. I don't really like wharncliffes. You get the idea....it has to fit into the style of knives I like for myself and that can be a broad range but it doesn't include everything.
Materials and construction - do I like the blade steel and way it's built (shadow vs bolsters and things like that)
I've been lucky to have a handful of customs pass through my hands recently and they've all been impressive in one way or another. There are tons of great makers out there right now doing some amazing things. The ones that I've experience recently that I've really like a lot are:
Ken Erickson
Reese Bose
Tony Bose
Bret Dowell
Dr. T
Shadley
There are others who I haven't gotten to check out in person yet but really would like to from what I've seen:
Pena
Hampton
Davidson
Oeser
Kawamura
(edit - forgot some....Dunlap, Coats, Lloyd....the list goes on)
Right now the custom knife that I'm carrying is a Ken Erickson. I really like his work, he has amazing variety and will take on just about any pattern...stuff you just don't see other people making in the custom arena. But, for me, it came down to just finding that perfect type of knife in his 3.5" spearpoint EDC pattern. I have two now, one in micarta and one in stag and the stag has moved into pocket duty displacing the micarta I have carried for months. Ken is a great person, a pleasure to work with, and he's relatively local to me here in Wisconsin. He also adds a small touch by making his own pouches for his knives, something I'm not seeing anyone else do. They are great pig skin velcro pouches and just add a really fantastic final touch to a handmade knife, so much better than the ubiquitous zipper pouch. It's a little thing, but it sets him apart in my mind.