Updated to include down to #14:
16 - N64 - Banjo Tooie (Nintendo)
15 - GC - Star Wars Rogue Leader: Rogue Squadron II (Activision)
14 - Wii - Metroid Prime 3: Corruption (Nintendo)
All but 1 of the remaining 13 games in my list was published by Nintendo... of the 37 games I have listed so far, 18 were published by Nintendo (in Europe), so slightly less than half. Although I'll admit I was surprised some of them were published by Nintendo. I tend to think of Episode 1 Pod Racer as a Lucas Arts game (similarly I thought the Rogue Squadrons were Lucas Arts, but in Europe they are Activision) Also before compiling this list I believed that Goldeneye was the only Rare game I owned that was published by Nintendo, but it turns out they all were.