How long of a HDMI cable to can run without any distortion effect?
also
How long for HDMI/DVI cables?

How long of a HDMI cable to can run without any distortion effect?

Hard to answer, but I believe that beyond approximately 50' you are taking your chances without some sort of amplifier/repeater. The distortion effect discussed here is probably the dreaded 'sparklies'.

How long for HDMI/DVI cables?

Same as above, HDMI and DVI use similar digital data. The connectors are different.

The HDMI spec has no limitation on cable lengths. We just dictate the maximum amount of signal attenuation allowed by the cable to ensure that the signal can be reliably decoded by the receiving device. If you read the threads on the forum, users are running 720p/1080i over 50 feet with a passive cable. I've personally seen 75ft run at this resolution over a passive cable. For 1080p, I've seen it run 15 m (about 45 ft). The quality of the HDMI receiver chip on the receiving device has probably the most impact with supporting a long cable run (via a good equalizer in that chip).

What about cable quality/thickness? 24g 28g @say, 10 meters?
If a bargain discount cable works, isn't it just as good as the expensive ones?

Our lab guys tell us that as a general rule of thumb, you do need to increase the wire gauge to support a longer distance better. When you start hitting those longer lengths (such as 10m), cable quality does become a more important factor in the signal integrity.