H.W.
I think AV's suggestion is correct: consider what the person who is originally speaking wants from the conversation. Sometimes, people aren't looking for advice, they are just looking for a bit of commiseration or empathy from someone they trust.
I've found that when I have stories, a night out with the ladies is often a better time to share those things than when someone is just wanting an ear. I also use "hmm..." a lot when to show that I'm listening - it's an acknowledgment which lets the speaker continue without really interrupting their own train of thought. And sometimes, a "Let me know how that works out" or "You know, I've had to deal with that too... if you want ideas, let me know"-- this extends the offer of advice without actually giving it unless it's wanted.