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I'm not actually opposed to DDA in all circumstances; as with almost everything in game design, it has its strengths and weaknesses. I think it's a great idea for simple, abstract casual games like the aforementioned Astrosmash, but the more heterogeneous a game's challenges are, the more difficult it is to create a DDA system that covers them all.
Any DDA system needs a performance-evaluation mechanism and an adjustment mechanism for each type of challenge that it will work on. The performance-evaluation mechanism determines how successful the player is at overcoming a particular type of challenge, and the adjustment mechanism makes the challenge easier or harder, usually by changing parameters that define the challenge (such as the strength of an enemy).
In Astrosmash, the performance evaluation was very simple: it looked at the number of lives remaining. You can easily do something similar with health points, money, or whatever other resource is critical to survival. Robin Hunicke has done some nice practical research on the subject using a Half-Life mod; see her paper "The Case for Dynamic Difficulty Adjustment in Games." (You'll have to create a free ACM account to download the PDF.)
If you're definitely going to use DDA, consider the following suggestions:
Make the game harder by beefing up the opposition, not by weakening the player. Players rightly feel that any power they have, they earned. Never arbitrarily take something away from a player; if they lose something they've gained, there has to be a reason for it. It's OK to make the AI more lucky, but not OK to make the player less lucky. If he's doing well and then suddenly finds that his sniper rifle no longer shoots straight, he's going to hate you.
Make it optional, as in Lego Star Wars II. That way the players who don't like it can turn it off. Lego Star Wars II actually offered both DDA and settable difficulty levels, but not everyone can afford to put in that much development work.
Make it subtle. I can't emphasize this enough. The same monsters that were easy to beat in level one should not suddenly be tough as nails in level two -- or vice versa. Big changes spoil the player's immersion and create inappropriate spikes or troughs in the perceived-difficulty curve. If at all possible, adjust the difficulty of the game through frequent small changes rather than one large one, so the player doesn't notice it happening.
Keep the details secret. Don't let your players find out exactly what performance-evaluation mechanism you're using, nor what the game will do to make things easier. Without this knowledge the players can't exploit the system so easily.
DDA is difficult to implement, complicates tuning, and your player may not want it at all. Think long and hard before you commit yourself to it.