Also, there is the matter of 1920x1080 being a 'proper' HD resolution. 1366x768 is an odd bodge-job res that seems to be a 16:9 'relic' version of 1024x768.
While 1360x768 is not a standard HDTV resolution, it is technically a VESA standard resolution (admittedly one not often thought of, but it is VESA standard), though 1366x768 is not.
I'm not sure I would call it a relic since just about every "720p native" LCD on the market have 1366x768 as their actual resolution. Why they do not use the actual 720p resolution of 1280x720, I do not know. My only guess would be that's is so they can support 1024x768 without scaling for better PC use - but you'd think being able to run 720p HDTV without scaling would take precedent over PC combatibility.
In any case, if a game supports widescreen resolutions, you can be reasonably sure it supports 1360x768. There's nothing that particularly distinguishes it from any other widescreen resolution.
I run 1360x768 on my HDTV and the only games I've had problems with, with one exception, are those that do not support widescreen resolutions in general. The one exception is KOTOR, however the issue there is not specific to 1360x768, the game has a general problem that applies to several of the lower widescreen resolutions.
There are a lot of systems that simply refuse to work with that resolution, even if they work fine with other ones, like 1280x768 and 1440x900.
Eh? News to me. The last 3 video cards (1 ATI, 2 generations of nVidia) I've owned supported it fine. I think it might be more accurate to say that many TVs do not support it, despite it being their actual native resolution - this is changing however.
Early HDTVs, despite using 1366x768 panels just like current ones, did indeed usually only support the standard HDTV resolutions of 720p and 1080i. However, newer HDTVs, at least good ones, increasingly will support 1360x768 through both VGA and HDMI (and they do not scale to 1366, you just get an unnoticable 3 pixel boarder on either side of the screen).
My Samsung for instance will support PC resolutions over HDMI as do all newer model Samsungs. Newer Sharp and Sony panels do too. Even cheap Olevia/Vizio panels often support 1360x768 over VGA at least.