What I'm about to say is based on the RBY generation, since I'm not familiar with other generations enough to comment yet.
Double Team on it's own is luck. However, it's all part of a Tank strategy - increase evasion and recover lost HP with Rest/Recover/Softboiled. This is a great way to make certain Pokémon (but only certain ones) increase their longevity and usefulness in battle.
Those who say Double Team (or the Double team/Rest combination) should be banned from battles (or that it's a "n00b" way of playing the game) are missing out on manipulating part of the game's mechanics to increase their chances of winning. Surely using any status/statistic-modifying move depends on luck? For example, lets say I used a Lapras's Confuse Ray to Confuse an enemy. I'm not just going to rely on the Confuse Ray working every turn - it would just be another part of my strategy to win, by decreasing the chances of the enemy getting a hit on Lapras. The same goes with the chance of not moving while Paralyzed - you wouldn't rely on it to help you win because it doesn't always work out that way, but it's part of the game's mechanics you can manipulate to increase your likelihood of winning.
So what's with all the evasion-modifyer hate? Are you saying that we should only use attacking moves that hit 100% of the time, so we won't be relying on luck to help us win? Even the amount of damage has an element of randomness to it, if you look into the formula used to work out damage ratios. In fact, why play at all?
Also, if you don't have a plan for taking out Double Teamers, you clearly need to do more training. I feel the same about people who refuse to battle against Mewtwo - if you don't have a strategy to take it down, then you need more work as a trainer. It's part of the game, so we should all learn to deal with it, and have fun working out how to counter the strategy of evading and recovering.
I'm not saying I'm a better game player than those who hate Double Team. I just think that it's an element of luck that works IN a strategy in order to make certain Pokémon more useful, and people who miss out on it because they refuse to rely on luck probably rely on it themselves to help them win matches, as I do.
If you've ever used an attacking move in the RBY games, you've relied on luck. Deal with it.