Here they are, in no particular order --
1. D&D (Holmes, Moldvay, Cook, 1st Ed., 2nd Ed.)
2. Champions (the original grey cover onward to the Big Blue Hardback)
3. Runequest (in the white box)
4. Tunnels and Trolls (the light tan version onward) w/ many solo dungeons of note
5. Warhammer 40,000 (the original book that fell apart)
6. Wizardry (on the Apple ][e)
9. Star Fleet Battles
10. Puerto Rico
11. Stormbringer (original version)
13. Fudge/FATE 2.0
14. Spirit of the Century
15. Swashbucklers of the Seven Skies
I'm sure I'm missing MANY board games but there you go... TALISMAN!!!
EDIT: Myst (can't believe I forgot it!) had a huge impact on me as a DM...