I hadn't put any thought to this until fall of 2015, so details before then are lost to time:

1st flight - Fall (Nov, I think) 1967; unknown AA CRP - DAL

1st TATL - Feb 1993; unknown DL DTW to LGW (ex-PanAm route - plane still had residual PanAm branding on parts of the interior)

1st European carrier - Mar 2007; AF (currently flight # 378, but I don't recall if that was the case at the time) CDG to DTW

1st inter-European - Nov 2009; unknown KL AMS to LIS

1st TPAC - Sep 11, 2015; AA 175 DFW to NRT

1st Asian carrier - Sept 12, 2015; JL 729 NRT to CGK (also 1st equatorial crossing; 1st inter-Asian & 1st 787)