My DS was 15 when he started dating a girl (same age) and the relationship quickly became quite serious, lasting nearly 2 years, before finishing when he was 17.1. I was concerned, especially as they were underage at first and because it was his first relationship that had lasted longer than a few weeks. I started to look at his texts when I could. It made quite shocking reading, confirming that the relationship had progressed sexually and it seemed that they were intimate at every opportunity they could snatch (not to mention the language). I have never let on that I read those texts, but I never felt comfortable when they were in the house on their own or in his room, especially as DS has a younger sister to set an example to.
Perhaps I shouldn't have read the texts, but I would rather know the score than be in the dark. DS is now 18 and I no longer read his texts because I now respect the fact that he's an adult entitled to his privacy.
Incidentally, I haven't read my DD's texts (she is now 15) but won't rule it out if something/someone happens which I am concerned about.
We have also had chats about strangers on the internet and not believing all that they tell you.
Best thing is to go with your gut instinct. If you are concerned (i.e. drink, drugs, sex, bullying etc), then you might feel it is necessary to look at their texts, otherwise I'd leave well alone.