I believe opera supports h264 mp4 format in html5 video.
I have opera installed in two different machine, windows 7 and windows server 2008 R2.
http://icsvideos.uh.edu/
this video can be played in window7 opera but cannot be played in windows server 2008 R2.

What is interesting is both opera is upto date and almost same version:

Window 7 Opera:

Version: 31.0.1889.174 - Opera is up to date
Update stream: Stable
System: Windows 7 64-bit (WoW64)
Browser identification
Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/44.0.2403.155 Safari/537.36 OPR/31.0.1889.174

Windows Server 2008 R2 Opera:

Version: 31.0.1889.161 - Opera is up to date
Update stream: Stable
System: Windows 7 64-bit (WoW64)
Browser identification
Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/44.0.2403.130 Safari/537.36 OPR/31.0.1889.161