Use case
When mapping cities, especially where there are lots of small streets/ways interconnecting, there are often some confusion where exactly is quest located in relation to user. Rotating the map, and using compass viewfield helps, but is not perfect (especially since compass/orientation sensor is not perfect in mobile phones).
Proposed Solution
What would help is (preference-enabled?) GPX-track drawn on the screen, so user can see where s/he's been prior to reaching current location.
(Something similar to OsmAnd "record GPX" mode), or this mockup:

Also, it would show user what streets have been traveled already and letting him/her decide where to go next. The GPX track could be removed if some amount of time had passed since it was last updated (maybe 6 hours? or 24h?), or could be left to user to clear it (for example, by disabling GPX option, and reenabling it later if s/he still wants it)
Alternatively, instead of full GPX track, only a last (few) hundred meters could be shown as disappearing trail (spacewar!-alike). While a little less useful, it would help with immediate orienting, and would avoid the issue of deciding when to remove displayed GPX track. Something like this mockup:

(I'm obviously not artist, the idea is the line is thickest and most opaque at the current location, and thins out and/or gets more transparent the father away it gets, and at far enough point it simply disappears)
This would maybe a nice gimmick. I have no objections against if someone wanted to experiment with an implementation. But I myself won't work on this.
Could be a nice tool to draw ways on the map by walking them...
Most helpful comment
This would maybe a nice gimmick. I have no objections against if someone wanted to experiment with an implementation. But I myself won't work on this.