My close friends don't but I get teased because almost strangers seem to tell me their life stories!!
I got stuck in a petrol station once because the attendant (who was always there but normally only said hello) decided to tell me about her illnesses (numerous) divorce, son, etc etc etc... Meanwhile I'm thinking I'm going to be late for work but it was so traumatic I didn't know how to pull away.
D's Mum on our 3rd meeting poured her guts out about his drinking, her marriage and plenty of other stuff too. Again, I needed it like a hole in the head but I so felt for her - all I could do was sit and listen, she hadn't had anyone to talk to about this for 20 years!!!
On holiday I get introduced to a circle of SL'an friends one of whom has a drink problem (1 in 5 over there so a bit hard to avoid). He then decides to tell me of a childhood full of abuse that then continued from his brother through adulthood.
Of all of these this one was worth something because he then told his other friends and although he still has a drink problem an enormous healing took place. They had guessed some of the stuff but just gathered round him as new 'family' and weren't angry anymore. The string of accidents one of which left him burned and another that left him without the use of his right hand started to make sense. Whether he winds up dead or not he got forgiveness and acceptance so I don't mind the emotional washing machine of him telling me first.
I work with kids in care and the same thing happens - more to me than other people I work with - just children telling me their lives.
Currently, because of the amount it happens at work I've asked to attend a basic counselling course - I want the tools to deal with it.