Dreamcast
Simple, elegant, and effective, like the console itself, this was a no-nonsense opener that announced itself and quickly scarpered, enabling players to just get on with it.
PlayStation
The all-time greatest? Maybe. That opening synth, that otherworldly backing track on the transition to the stark PlayStation logo. The fact that it pretty much gave you the audio/visual cues you needed to run import games. The best.
PlayStation 2
PS2's startup screen took everything great about the original and pushed it to the very limit of twattery (which, naturally, would reach its nadir with the PS3). Yes, it was a bit pretentious, a bit weird, and, when your disc drive invariably failed, utterly infuriating. But seeing it for the first time was an experience, even if that experience was 'what is going on?'
Xbox 360
The subject of many dashboard (and startup screen) revisions, the 360 had some memorable openers. Whether it was the giant X crashing into a sphere, carving itself into it, or the vaguely Dreamcast-style revision seen above, Microsoft certainly learnt its lesson from the utterly abject boot screen of the original Xbox (see below).
Gamecube
Deliberately cutesy, yes, but this intro states the purpose of the console – or, its platform holder, really – well: it wants you to have fun. The cube rolling around to form the G is a nice touch, but this intro really came into its own when you were playing something like the Resident Evil remake: the joviality of that opening only heightened the horror that came next.
Game Boy
As in the above video, the first time many of us saw this logo it was immediately followed by Super Mario Land. Quick and to the point, that ding sound was the equivalent of a digital wink, letting you know everything was going to be fine. Unless you were playing Mortal Kombat 4, of course.
Amiga 500
In here for both pure nostalgia value and for its iconic imagery, the Amiga boot screen was a thing of beauty.
Special bonus mention: Saturn
Alright, this was a blunder on our part. Heady with nostalgia, we forgot about this one, which is excellent. Sorry. We failed. Like the Saturn.
Dishonourable mention: Xbox
Words can't do justice to the colossal magnitudes of awful witnessed here. If you were to ask people what they thought alternate future Space-Chernobyl looked like at the moment of meltdown, it might look something like this.