I've been home brewing for a little over two years, now, and an auto-siphon has always been part of my kit. Last fall, I had to replace my original siphon because the valve at the bottom of the tube popped out and I couldn't get it back in. I just racked a batch to secondary on Monday and the same thing happened again before I even managed to get any beer moved.
This time around, I tried harder to get the valve back in to place and I actually managed it, to my surprise. Unfortunately, the valve wouldn't stay mounted anymore so it was impossible to start a siphon.
Auto-siphons are cheap, sure, but you apparently get what you pay for.
I've looked around a bit for how to rack from a bucket without an auto-siphon and this thread has been the most helpful. Manually starting a siphon with water, sanitized water, a turkey baster, your mouth, etc. seems like the best thing to do; obviously use sanitized means before unsanitary means but it's good to know what can be done in a pinch.
If you're looking to rack out of a carboy,
this thread has a great set of steps with pictures. The poster mentions preferring sucking on the cap to start the siphon is better than blowing but blowing is considered safe enough if you do it gently so as to not disturb the CO2 blanket.
Try not to drool in to the cap or hose
Cheers!