Interesting question, certainly one that's being debated endlessly on Internet forums everywhere as we speak. At the moment, I'd have to say that the XBox 360 is in the best position, which of course could change dramatically a year or two from now. By getting their system out a year before the other companies, Microsoft has put themselves in excellent position to grab a large market share, in much the same way that the PS2 dominated the last generation by being the first one out of the gate. The 360 launch was notoriously bad, but with no competition in sight, that wasn't too much of an issue. With second-generation 360 games on the market right now that look AND play better than first-generation PS3 games, it's going to be tough for Sony to make headway among hardcore gamers, at least in the immediate future. Since the 360 also costs less (and we know a price cut or bundle deal will be coming after Christmas in 2007), and has better online service, and has many, many more games (exclusive and ports) right now, there's just no logical reason right now to buy a PS3 over a 360.
The PS3... a year and a half ago, I would have said there was no possible way for Sony to screw this thing up, but things just don't look too good right now. Clearly, their biggest problem was assuming that everyone would buy the PS3 regardless of price, just because it had the SONY brand name on it. Based on that assumption, they decided to use the PS3 as a trojan horse for their proprietary Blu-Ray Disc format. Now in theory that sounded like an unbeatable combo, but adding Blu-Ray skyrocketed the cost of the PS3 (it actually costs over $800 to make) and has resulted in massive shortages and production delays. Even worse, the highly touted Cell processor is apparently extremely difficult to program on, and (perhaps the absolute killer) PS3 games do NOT look noticeably better than 360 ones. In fact, many ported games actually look BETTER on the 360 than on the PS3 right now - not exactly the best news for such an expensive, high-end console. Not to mention that only people who have very pricey HDTVs (roughly 10% of the population) can even make use of many of the PS3's graphical features.
Here's what I'll never understand: the PS2 was the most successful console of all time (over 120 million sold) because it reached out beyond the core base of hardcore gamers to reach mass-market status with casual gamers. People who never play games (like my brother, girlfriend, etc.) - they all have PS2s. Yet when Sony designed the PS3, somehow they deliberately priced the system outside the range of what casual fans were willing to buy, instead designing a console that appears to cater to the high-end, early-adopter (niche) crowd. God alone knows why they would do something like that... arrogance and greed are the most likely answers.
I haven't mentioned the Wii at all, most because I have no clue how the system will do. Clearly it's doing outstanding right now, with tons and tons of positive buzz surrounding the console. The real question is whether Nintendo can maintain that momentum once the initial novelty wears off, in 2007 and 2008. There are a lot of developers lining up to program for the Wii right now, but Nintendo has been very poor in that regard of late, so the verdict is still out. Whether casual gamers stick with the Wii will largely determine its overally success; if Nintendo can effectively tap that market, the system has the potential to be a gigantic success. Even if the Wii would "fail" by capturing only 33% of the market, Nintendo would still rake in the cash, so the Big N looks to be pretty good shape right now. (As opposed to Microsoft's XBox division, which in 5 years has NEVER turned a profit in any fiscal quarter, or Sony's SCE division, which is projecting 1.7 billion dollar losses for the upcoming fiscal year.)
I see both the 360 and Wii doing well in the immediate future, with the PS3 being some distance behind. It's possible that the PS3 may pick up in sales down the road, but at least initially the system is going to lag FAR behind the other two. Sony is already selling the system at a massive loss, so a price cut seems unlikely in the near future, and all of the most-desired PS3 games won't be coming out until late 2007, at the earliest (and some of the "exclusives" may no longer be exclusive by that point in time). If system sellers like Final Fantasy XIII and Gran Turismo 5 don't come out until 2008 (which is looking quite likely), the console war may already be over for all intents and purposes by that date, because gamers aren't likely to wait another full year before purchasing one of these consoles.