All the mario karts as far as I know (maybe not snes). As mentioned already half life 2 and episodes changed according to what part of the game you were up to, as did portal 2. portal 1 and 2 had different title screens after you finished the game (not sure if they stayed that way though...)
Yoshi's Island - The title screen changes to a night-time scene when you complete it. StarFox 64 - I seem to recall earning all medals on Expert difficulty changed something about this...maybe just the ability to move the "64" logo around with the analog stick.
Didn't Super Mario World also change the title screen after you complete it 100%? I'm not sure if I remember correctly, but I think it changes the Koopas to those Mario-Koopas.
Killer7 changes the title screen to "killer8" after completion.
The title screen of Jet Force Gemini actually changes several times. Each time you unlock a new character they are added to the title screen, and when you defeat the final boss it relocates them to the city.
In Hitman: Blood Money the camera moves after you complete each level, to give you a different view of 47's
I (kind of) remember Devil May Cry 4 giving you an alternate title screen after completing it. Dante and Nero on a sofa, and another one Dante and Trish sitting on/at a desk in Dante's office... Although I could have dreamed these?
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