Here's a simple demo but with an interesting trick:
Grenian (use gren_old.wad) by William Green, UV Speed in 0:25. [Note: doesn't work with the later version of this wad that is in the standard archives.]
I'll quote from the text-file:
This is a fairly simple demo, but illustrates what I think is a new, or at least little-documented, trick.
The trick occurs near the start of the demo, and enables me to get the blue key without getting stuck (the platform it is on is meant to lower, trapping the player, but I manage to avoid triggering it). Note that this is not a simple case of strafe-running over a linedef. I have not managed to do so at all with -nomonsters - it seems to be the interaction with the monsters that makes it possible.
I'll call this trick a "thing wobble". It may well be related to the well-known idea of "thing-running", whereby a wallrun-like effect is achieved in a west-to-east direction by running along a row of "things" (e.g. the barrels in Doom2 map23). However, there is more to it than that, and I think this trick has wider applications. (It may also be related to the form of grab seen in, e.g., Ultimate Doom E4M1.)
I believe the effect is as follows: when the player is running hard up against a "thing", the engine calculates his momentum as if he were actually running. Thus when the thing ceases to be in the way (e.g. it moves, or the player slides off it), the player's speed is as if he has had a run-up, rather than as if he had started off from stationary. Added to that, there is the possibility of a "thing-run" effect, if the direction is right.
Therefore in this demo, it is as if I have achieved a wallrunned S50 with a run-up - and this gives me enough speed to skip the linedef. (There is a similar set-up in this map with the red key - there I have been able, very occasionally, to get the same effect with -nomonsters using a actual wallrunned S50 with run-up, but my success rate is actually worse than for the blue key trick.)
I have included in the zip two other demos where similar effects are relevant. In C232P030 I make use of the thing wobble (though that jump can actually be made with just S50, I think), and MW11-036 is a weird demo that I still don't understand, but I manage to avoid triggering a linedef while wobbling up against a monster, so maybe it is related. (It could be more closely related to the E4M1 grab though - with quirks in the positioning system causing the engine to fail to see the player crossing the line.)
So, what are the possible applications of this trick? In addition to skipping linedefs, jumps off ledges could be done in this way. There is no scope for a run-up in that case, so a jump that would otherwise be impossible (or need rocket assistance) could be achieved using a thing wobble. The "thing" can take the form of a monster, a "thing"-based piece of decoration - or a coop partner.
I'd be interested to hear if this idea has been previously documented or consciously exploited, and if anyone can shed more light on the mechanics of it.