Which system will dominate the next couple of years? When it comes down to it, it's what system has the best games, not how powerful the system is. I actually think the Dreamcast has a pretty good chance for success, as long as Sega gives us the games we want. They have gotten a good list of developers for it (Game Arts *yipee*), and overall, I like the games they make.
Sony has basically already sold a billion PS2s in America. I remember the main reason why I got a PSX was for Final Fantasy VII, and that very system brought (and is still bringing) me favorite games such as Xenogears, Lunar:SSSC (soon Lunar 2:EB), FF7, FF8, and Grandia. Remember when the Playstation first launched? Everyone thought it would be another 3DO, which brings me to the X-Box...
Microsoft chairman Bill Gates announced plans for the X-Box at the Game Developers Conference last week. The question is, will anybody buy it? Well... I think both yes and no. PC gamers and console gamers are two worlds apart, and I think it will be a dream come true for western game developers, because of the low development cost. If the X-Box is to succeed, it needs good games, period. It may have the western developers, but what about the Japanese ones? It needs developers like Capcom, Namco, Konami, Square, etc. It's supposed to be 2x the speed of the PS2, so it's gonna be a powerful piece of machinery. I think it has a good chance if it can get decent games on it.
Nintendo's Dolphin (what happened to the U.S. 64DD?) is almost certain to sell a lot of systems? Nintendo's games are enjoyable, they have a lot of money, and they've got Poke'mon. The N64's downfall was its lack of third-party support (it still doesn't have a decent RPG or Fighter), and that they chose to stick with the cartridge format. They've got to get it together if they want the Dolphin to be a success.
My conclusion is that all the systems have a good shot at succeeding, if they get AAA titles. I play games for the fun of it, and I'll play the system with the best games. I think they're only gonna get better. ^_~