When considering the question I realized I have not used a random encounter table in ages. That does not mean that I do not use encounters that are not related to the plot. Either I think of them right at that moment, which mainly happens in cities or I have got a list of several encounters I wanted to use one time or another and decide to use it then and there to bring some life to the game. It is as people have said, random events and encounters bring a world to live because the players get the impression things happen outside their influence.
There is a strong risk though that a random encounter has such a strong pull on the PCs that they ignore the real adventure and chose for the random encounter as their focus. This is all fine and dandy, but in many cases that was not something the DM has prepared for. Secondly, a random encounter could disrupt the mood of a session. When the players have been tensely into roleplaying a fight sometimes can be a good thing but at other times it can be very destructive of the mood.
For this reason I prefer to have full control over when, where and what when it comes to encounter. I used to use the tables in the past to pre-generate encounters. Now a days I just think of a few that sound logical without rolling any dice.