What's the difference between 了, 著 and 到 when used as verb complements?
了 and 到/著(着) (zháo) serve different functions in sentences.

了 used after verbs implies a sense of "stopped, finished,completed, or done" on the action. 

到 and 著(着) used after verbs indicate the result of the action. 


  
  找(不/得)着, 找(不/得)到
  够(不/得)着, 够(不/得)到
  吃(不/得)着, 吃(不/得)到
  


I can't really tell the difference between 到 and 著(着), but it seems to me that 到 sounds a little bit more formal than 著(着). 

In some cases, 著(着) seems emphasizing on the ability of doing something, while 到 seems focusing on the result of doing something.


  
  书架最上层的书，我够不着. vs 书架最上层的书，我够不到.
  我跟你说话呢，你听不着吗？ vs 我跟你说话呢，你听不到吗？
  家里有这么多活儿，你看不着吗？vs 家里有这么多活儿，你看不到吗？
  你打不着我. vs 你打不到我.
  找不着北了. vs 找不到北了.
  


But there are some cases where one is more likely used than the other.

Case A) In the following sentences, using 到 is good, but using 著(着) sounds awkward.


  
  这个办法, 我早想到了.
  演唱会的门票, 我终于搞到了.
  这个赌, 我最终赢到了.
  


Case B) In the following cases, only 到 is used.


  
  说到做到.
  说得到做得到.
  说得到做不到.
  请同学们说一下,你在这幅画中看到了什么, 又想到了什么.
  尽到责任.
  货送到了.
  话我是带到了啊，去不去由你.
  收到信了.
  受到好评.
  遭到敌人的伏击.
  


Case C) In the following examples, only 著(着) is used, to show something (not) getting into a continuous state.


  
  他睡着了. 
  他翻来覆去睡不着. 
  出了这么大的事他居然还睡得着觉.
  他的衣服烧着了.
  他把油灯点着了.
  油灯没油了，点不着了.
  他把炉子引着了.
  他把发动机起着了.
  他把打火机打着了.
  打火机坏了，打不着了.
  


Case D) In the following examples, only 著(着) is used.


  
  我爱怎样怎样，你管不着(or 你干涉不着).
  有话好好说，用不着这样鼻子不是鼻子脸不是脸的.
  这事儿还真让你说着了.
  哼！这次算你捡着了，下次可就没这么好运了！
  丈二和尚，摸不着头脑.
  


Case E) When there are place/time coming after verbs, only 到 is used.


  
  爬到树上
  睡到天亮
  牛皮吹到天上去了
  你这话说到我心里去了.
  你这话，说到点子上了.
  


Case F) When there are objects coming after verbs, in some cases both 到 and 著(着) are ok.


  
  我没碰着他. 我没碰到他. 
  我没见着他. 我没见到他.
  我没买着那本书. 我没买到那本书.
  再也吃不着这样好吃的菜了. 再也吃不到这样好吃的菜了
  


But in the following cases 到 is more preferrable.


  
  听到一阵枪声
  看到一块巨石
  


By the way, 着 (zhe) is used to descibe a continuous action.


  
  看着她跳舞
  打着手势
  撇着嘴
  


Note: I polished my answer with some good points from other answers or comments.