This is a software solution to remote page turn on a kindle. In brief, I am running a webserver from my kindle. This is serving a cgi script which imitates a button press on my kindle. I access the scripts from a browser on my phone.
This means that my hands don't need to be near the kindle when turning pages.
For me, this is an ideal set-up for reading in bed: my hands can be under the covers while the kindle itself is on a stand, but I don't need. It may also be helpful for those who find it difficult to hold the kindle themselves, or to control it using the built in buttons (see, for example, this modification http://hackaday.com/2011/08/24/more-frankenkindle-progress/ )
The kindle you use needs to be jailbroken, and needs to have physical buttons (The specific method used here simulates a button press, but it may be possible to adjust the scripts to work with touchscreen kindles as well -- let me know and I'll add it to the instructable).
I am using a Kindle 4 NT, and this guide will be tailored to that, but it shouldn't be too difficult to adapt the process to other models.
For the remote control, I am using an iPhone 3GS, but all it is doing is accessing a web page, so it should work with any smart phone (in fact, any device capable of accessing the internet within your local network -- you could even control one kindle with another, although I'm not sure why you'd want to, exactly).
Now, on with the instructions.
Step 1: Jailbreak your kindle
(Image from http://wiki.mobileread.com/wiki/File:Kindle4NTdiagnostic.jpg, by Needsleep99, licensed under Creative Commons Attribution Non-Commercial Share Alike.)