Hi everyone who may read this in the future. I came upon this thread when looking to remove my picture rail from my wall. I just wanted to share part of my method with small variations depending the tools you have on your disposals. This method makes the assumption that glue has not been used to fix the picture rail.
The minimum tools you will need are:
Small jemmy,
Hammer
Stanley knife
Saw
Tools that will make your life easier include heat gun (to remove easily paint), drill and plumbers hole saw set.
Start of with using the stanley knife and cut through the paint across the top and bottom of the picture rail, where the picture rail meets the wall. Then have a look on the surface of the picture rail and you will identify small indentation. It is likely that these are the positions where the nails have been put through the picture rail. If you want to be certain you can use the heat gun to remove the paint, though not necessary. Once you have identify this positions, you can either use the normal saw and cut the picture rail on each side of the nails. Alternatively you can use the drill with the plumbers hole saw, to cut around the nails. Then use the small jemmy and gently try to move the picture rail off the wall. If you find it difficult to remove the picture rail, it means you have missed some nails. Once you have done this and removed the picture rail, you will be left with the nails and small amount of wood around the nails. Use the jemmy and hammer to remove the wood left around the nails, so you are left then only with the nails. You can use the small jemmy to remove the nails. DO NOT try to use any force directly on the wall. As suggested in a pervious comment use pieces of the picture rail between the wall and the jemmy, so the wall is not damaged. You will hopefully be left with tiny holes on the wall.
I have to say that this method is not my own invention but brings together some of the comments before me and the credit should go to those who kindly shared the knowledge previously.
Also i am making the assumption that you do not wish to keep the picture rail.
Good luck!