Interesting Discussion, And Forum :)
I think it depends what "backtracking" is defined as, do you mean ANY time you return to an earlier area, or just when you have to go back over exactly the same "terrain" as before? I'd agree that the latter is generally bad at any prolonged distance (I don't think a few rooms or something like that matters and it can help add a sense of place). But based on my favorite game levels of all time I think the former is near essential. Sometimes it MAKES a level for me when I leave a room after seeing an area that I don't think I'll access, then 20 minutes later I enter an area and I'm suddenly like "cool!" when I realised I'm at the area I saw earlier and nearly forgot about. I agree with what someone said earlier though that (unless it is really necessary), splitting this style of area over multiple maps lowers the effect as it feels more fake (although I would still consider it preferable to not seeing an old area at all).
It's also a balance though, on a single level I would always support using a "guided non-linear" style, but in a big pack it could pay to mix things up a bit, and follow up a non-linear level with a "straight-line" one for a little contrast.
Levels that I like tend to be almost overwhelming at first, you see some huge environment and are like "how the hell will I explore THIS?", but then you are taken along the path to kick progression off (perhaps via story directions or something) and it suddenly flows like water (while still providing plenty of room to go off the path and explore side areas) and you wander why you were ever overwhelmed in the first place :P .
Although a mapper shouldn't necesarily focus on it much, if at all (where's the fun in it if the mapper had already decreed your route?) but a guided non-linear design also has the bonus of leading to cool tricks etc for crazy speedruns and stuff like that.
As for things like jumping along the main route I think a few hops add to the atmosphere if you are running from a collapsing building or something, but jumping puzzles for the sake of it on the main route generally do suck (although even that can depend on the situation).
To pull out of example of what I think are horrible level layouts I choose the majority of the "Anti-citizen one" levels in Half Life 2 .
Firstly the path is a straight line, not necessarily bad if done right, but this chapter of HL2 varies the gameplay very little, it's just shooting the same two or three enemy types over and over with the odd (contrived) headcrab encounter thrown in, there are also very few puzzles or other things like that, the only slightly varied thing is the use of the "hoppers". Other than a few windows stuff like vertical combat is very rarely introduced, it's all blasting the same stuff on the same level as you, which further adds to the monotomy. Also, although it is set in a city there is little "rhythm" to it; you go through an apartment and suddenly end up in an underground car park, it's like they couldn't think of a convincing way to do a transition. Other than the Citadel (which is seen throughout almost the entire game, so I don't necessarily count it as a "unique" addition considering it's pretty much just a cool skybox detail) there is very little forshadowing, you just pass through an area and that's it, it's never seen again.
As a "solution" to all this I think it either should have just been a lot longer and with more complex (and interesting) means of progression past each area, or it should have put you much closer to the Citadel, and focused on a smaller but much more "fleshed out" area.
On the flipside the next chapter, Follow Freeman, I'd probably consider one of the best done in the game. Especially in the "museum" area; you enter a structure (with a task that is non-linear), then come out the other side and return to the courtyard area again, which is now completely different.
Funny how my first post is a huge rant, but as the quality of level design in a lot of recent "retail" FPS games has been IMO terrible for the most part, yet people insist on calling parts I consider horrible "great" I've started to be pretty passionate about it :P .
Some further clarification on what I believe on this Unrealsp.org article; I agree with almost all of it, "Conceptual Grandness" is the key!: