The Hobby-Eberly and SALT telescopes have (slightly) non-round mirrors that operate at fixed altitude: http://www.as.utexas.edu/mcdonald/het/het_gen_01.html

You might also find the Large Zenith Telescope interesting: it has a spinning liquid mirror! http://www.astro.ubc.ca/LMT/lzt/index.html

Related question: is it possible to build cylindrical reflectors (more precisely, two dimensional reflectors with a constant parabolic profile along X axis), gather the light into a linear CCD array and do the Y axis focusing in software?

Reason: this will allow us to fabricate mirrors either by bending planar materials or by using a grinding tool that has the shape of the full parabolic cross section. Theoretically this should be a lot cheaper than the grinding methods we use now.

Why would that be easier to build?

Edit: I'm asking because I'm pretty sure it wouldn't be.

Less weight to support per ground area, the mirror would not sag as much.

Do you mean building a 5 meter wide oblong mirror instead of a 5 meter wide circle? That might be easier but wold be a far inferior telescope. The amount of light collected goes as the area of the mirror. If you're suggesting keeping the same area but being more oblong, then I don't see any advantages.

I did mean the same area. The advantage is that since it is longer it has a larger footprint.

Meaning more support, which to me seems easier to build (mechanically, don't know if the optics themself will be more complicated - that was my question).

I think a big challenge would be that it would be much harder to grind the mirror. Round mirrors have the advantage of being somewhat close to a parabola, so you can spin them and use gravity and then just refine from there. The optics also get more complicated.

One key thing that I think would help you here is that the hard parts of building a telescope are the mirror and the instruments, not the mechanical telescope to support it. Supporting a ten meter wide mirror is not too hard compared to making a near-perfectly ground mirror that is ten meters wide or building top shelf instruments to collect and study the light. It's not cheap or anything, but it's not really what's holding back telescopes. You can see this in the new generation of 20-30 meter scale telescopes with multi-mirror designs. The GMT uses several 8 meter mirrors because we can't really make useful mirrors larger than about 10 meters.