It's all down to personal opinion, of course, and to me it's the N64, simply for three games; Goldeneye, Perfect Dark, and Conker's Bad Fur Day (CBFD for some of the multiplayer modes, which I can (and do) replay endlessly just against the bots). Yes, PD is on the 360 (along with the *massively* disappointing sequel, Perfect Dark Zero), in the form of a high definition update from XBox Live Arcade, but some of the changes they made are for the worst, so I prefer the N64 version), and CBFD was sort of remade into Conker: Live and Reloaded, for the XBox, but they removed the great (and the not so great) N64 multiplayer modes, and replaced them with a very inferior (I and many others think) multiplayer mode, so I never bother with the XBox version.
In both cases (PD and CBFD) I *much* prefer the N64 versions, and of course the current generation cash-in-on-the-name Goldeneye game from Activision wasn't even one percent as good as the N64 version, so again it's the N64 version for me. These three are by far my most played games ever (even though I have a PC and six different consoles) and make the N64 the best console to me, and the one with the best exlcusives (even though PD isn't technically exclusive now).
Bung in other N64 exclsuives such as Duke Nukem: Zero Hour, Body Harvest, Space Station: Silicon Valley, and others and the N64 is great for exclusives. Not as many as some consoles, admittedly, but to me it's the best.
"PCs don't catch viruses or malware. Stupid users do." - The Cranky Hermit. For all things N64: http://z9.invisionfree.com/Nintendo_64_Forever/
Banjo Kazooie (Not counting the xbla version since it wasn't during the same generation) Conkers Bad Fur Day 007 Goldeneye Body Harvest (Best game ever made) Mario Kart 64 Pokemon Stadium 1&2 Ocarina of Time Mario 64 Yoshi's Story Turok 1&2 Lylat Wars/Starfox 64 Smash Bros Perfect Dark 64
Nintendo systems always have the most exclusives that appeal to my tastes. The other systems tend to have much more third party support, however, so there's always at least a few exclusives on those systems that I like.