Flying with your bike I am going away on a cycling holiday to the Alps and need to take my bike on the plane with me. Has anyone had experience taking bikes on planes and how did you protect your bike?

Can anyone recommend anything which will solve this problem?
There are two schools of thought.

1a) Bike box:  This is a hard shell, fairly large box that with wheels, pedals removed, and handlebars (disconnected at the stem) put to the side fits your bike.

From a safety of your bike perspective this is pretty protective.  I have used this approach flying within the United States, and over to Europe.

You will almost certainly be charged by the airline extra. At one time membership in the US's Mountain Bike association (whose name escapes me) had a deal with many airlines to waive the fee. 

1b) Paper bike box: Sometimes you can buy these at airports (Call ahead), or else many bike stores will let you grab one from a new bike they recently assembled.  (I know taking Via Rail on Sunday from Ottawa to Toronto they sell them for $10 at the train station).

2) Bike bag: By using a soft bag, it implies to the luggage handlers, be gentle.  I know people who travel with bikes who swear by them.  Again wheels and pedals removed, to minimize size.  

I am not personally convinced that luggage handlers at airports around the world really feel that way.

You will still likely have to pay an oversized luggage fee.

In both cases, many airports have different luggage carousels so it will probably NOT come off with your regular luggage, so look around or ask where that might be.  I have seen as nice as a specially marked obvious area, to an unmarked door you have to wait at. 

Also, some smaller planes might not have room for your box or bag, so they might send it later, making you wait for it, depending on how your connecting flights work out.