First consumer-grade LCD computer monitors were released around 1997, but they were mostly 5:4 and 4:3, and still very rare. It wasn't until 2004 that 16:10 came along, with 1280x800, 1680x1050 and 1920x1200. 1920x1080 came a year or two AFTER that. First time LCD monitors outsold CRT was in 2007. 2008 was when 1920x1080 began to reach mainstream TVs and monitors.
More of a side note:
All in all, I think most people are grossly overestimating the ubiquitousness of 1920x1080; in reality, it hasn't even reached its peak, yet. It's still less than 10% of users. Anybody can think what they want, but 1920x1080 probably ain't disappearing anywhere for at least 10 more years... What we're seeing here in a hobbyist forum is far from what the actual situation is. Here's a quote from one of the sources I used: "
1980×1080 exceeded 9% in May 2014 and may become the most popular screen resolution in the next years!" ... Yes, that ubiquitous. My guess is that it will peak in about 6 years, after which it will slowly decline. Also, don't mix up RELEASED new monitors, SOLD monitors and USED monitors.
I bought my last CRT (22", 4:3, 800€) in 2002, because the LCD tech was still so poor, at the time. That CRT in particular COULD display 2048x1536, but I used 1024x768 and 1280x960 for higher refresh rate (and fps). IIRC, it could do 1024x768@160Hz and 1280x960@120Hz.
Actually, even my earlier 19" 4:3 CRT (which was bought in 1998, not sure when it was released) could indeed display 1920x1080@60Hz (not sure if it was possible with the drivers or OS of that time, but it worked with the generic Plug-and-Play drivers from 2013, at least).
Here are few sites I used as source (if you don't feel like checking more than one, then I would recommend the last one):
http://www.pcworld.com/article/209224/historic_monitors_slideshow.html
http://www.vaughns-1-pagers.com/computer/video-resolution.htm
http://www.ehow.com/about_5459113_history-computer-monitors.html
http://www.teoalida.com/miscellaneous/monitor-sizes-screen-resolutions/
Ps. As for games, I don't know. But didn't some games after-2000 simply list the resolutions that the DirectX gave them as possible resolutions? So, if you managed to get DirectX to accept 1920x1080, then those games would allow it?