Did the Buddha really say that "life is suffering"? I often see the first noble truth (duḥkha) stated as "life is suffering". I have yet to come across a passage in a Buddhist text which phrases it like this - mostly they don't talk about "life" in this sense. So where does the idea that "life is suffering" come from? 

There's been some discussion about the definition and translation of the word "dukkha" also. Is there a definitive definition?
The first noble truth is actually amazingly relatable for the most part, as in no reasonable person could find fault with it. Since it doesn't appear to have been mentioned, I will post a full literal translation of the first noble truth from the Dhamma­cakkap­pa­vat­ta­na­sutta:


  jātipi dukkhā 
  Birth is dukkha
  
  jarāpi dukkhā
  Old age is dukkha
  
  byādhipi dukkho 
  Sickness is dukkha
  
  maraṇampi dukkhaṃ
  Death is dukkha
  
  appiyehi sampayogo dukkho 
  Association with the disliked is dukkha
  
  piyehi vippayogo dukkho
  Separation from the beloved is dukkha
  
  yampicchaṃ na labhati tampi dukkhaṃ
  Not obtaining one's wishes is dukkha
  
  —saṃkhittena pañcu­pādā­nak­khan­dhā
   dukkhā.
  In brief, the five clinging aggregates are dukkha


People have a tendency to focus overly much on the final one, which is terribly difficult to translate into english, it can be explained but can't be rendered in a pithy way which does justice to the meaning. Putting aside that which is difficult to translate, the rest of it is very straightforward, and are about the actual physical and emotional sufferings in life we can all relate to.

These points are easily understood at a conceptual level, and make an excellent starting point of investigation. For example with the emotional pain of "being separated from the loved", I noticed I would experience a piercing pain the chest in association with being rejected by someone I loved, and I would note that that person was not in fact stabbing me in the chest and that therefore the painful feeling warranted serious investigation since it did not make sense.

It should be noted that the first noble truth does not make irrational statements such as "Association with the beloved is suffering", we may reason that being separated from the loved is inevitable and so that kind of pleasure is like a honeyed barb, it is pleasant at first but will cut us later. Nevertheless the first noble truth does not deny the reality of that pleasure.