I've worked with 2 strokes, 4 strokes (including Miller Cycle versions), and rotaries.
The two strokes hit a wall pretty quickly. They are very rev-happy, but their combustion leaves a lot to be desired. Most lack conventional valves and rely on ports to move the mixture around. You can supercharge them, but I've never been able to do so properly. Once the engine size starts to increase, their main advantage (RPM capabilities) start to diminish. Plus their combustion is not very clean, due to the lubrication being part of the fuel. They are fun when modified, but noisy. Ask my neighbor (who gets to enjoy the glorious sound of the modified 2 stroke in my weed whacker).
The 4 strokes suffer from harmonics, weight, and packaging issues. But they can be supercharged without much problems. You can get at least 100 HP/Liter on a 4 stroke engine without much issue (when you build it properly, of course). Building a 1,000 HP 5 liter engine can be done by buying off the shelf parts. The problem is that when harmonics start dancing to the devils fiddle, your valves start to drop, and your pistons shatter like the dreams of those who bought ENRON stock.
The rotary is my favorite racing engine. It doesn't drop valves (it lacks them). You can scale them by bolting on more rotors (12 rotor beast here: http://i436.photobucket.com/albums/qq83/Adam-Blackshaw/12rot...). They rev like crazy and feature few moving parts. But they are hard to tune properly, and tend to run a bit hot if not maintained correctly. Mazda built, raced, and won Lemans in 1991 with a 4-rotor equipped car called the 787B. Which sort of proves that they are viable engines. The real problem is emissions. The rotary has not received as much R&D as the 4-stroke, and thus it is a bit behind. Further developments by Mazda have improved it, but I don't see it lasting too much with the future CAFE standards looming over the horizon. It is also not very fuel efficient, due to it using ports rather than valves. Though I'm curious as to how a direct injected rotary might improve all of these issues. Not sure if I will ever see it happen.
Before you call me biased towards the rotary, let me tell you that I do not, or have ever owned one. I have worked with them, and got to enjoy it very much. My current favorite engine is the Porsche flat 6, because the damn things will take any boost you send their way.