STAR STREAKS: The phenomenon we see of streaks passing by when a ship is at warp.A possible explanation is that we see stars passing by. However, this is disprovable: Some extreme speed we saw in TNG was 788,940c (I can't confirm the episode name).
This would give a characteristic angular speed for nearby stars of 1578 arcseconds per second or 1 degree every 2.3 seconds. This is indeed verified in simulations. Travel at high warp speeds, on the TNG warp scale, does not match very well the appearance of the bridge view screen on a typical episode. Indeed, most visible stars are not nearby but are further away with correspondingly lower angular speeds. I offer no solutions to this discrepancy other than the dramatic necessity that stars wooshing by at high warp speed.
There's a lot of support on rec.arts.startrek.tech for the notion that those things aren't really stars. For one, as the Enterprise drops out of warp (with the camera tagging along for the ride) some of the 'stars' do some pretty strange things, such as suddenly angling off in various directions, disappearing, etc.
Also, in 'First Contact', the Phoenix barely breaks warp 1 and stays relatively close to Earth, but we still see the streaks. Definitely not stars.
The predominant theory is that what we're seeing are free particles in space interacting with the expanding boundaries of the warp field. As they ross the warp field, they are repeatedly accelerated to FTL velocities and then slowed to STL speeds, and start spewing out something like Cerenkov radiation, a (real!) blueish light emitted when particles moving faster than the local speed of light (in a dense medium)are forced to slow down. If not exactly Cerenkov radiation, then something similar.
An other theory is that the streaks are part of the visual manifestation of Einsteinian space in subspace.
As a side note, in 'The Cage' (TOS), the moving particles seen through the forward viewscreen are explicitly identified as meteoroids.
How much of this stuff is "canon" is somebody else's guess, but I favor the microscopic particle theory, myself. It makes sense. What other theories do we have for the "starstreak effect"?