Anno, I always ask when I check in if my baggage will be transferred for me but even so it doesn't always work. When I went to Phuket on my way home last year, the Phuket -Singapore flight was late so I had to run through the airport to catch the Heathrow flight. They told me just before we landed that my bag had not made it, but it would be on the next flight. However, I had to catch my flight to Geneva, so they sent it on to Geneva airport and I picked it up the next day. It was ruined, but they sent me a new one which is a much more expensive make, but weighs 5 kgs when empty.
I was a bit tense coming back this time, as I had only 2 hours between the landing time from Singapore at Heathrow, and the Geneva flight, but it worked out. I did wonder who would be responsible if I missed a connecting flight because the previous flight, with a different airline, was late. I must ask Singapore airlines about that.