Kitchen safe touchscreen recipe reader
I've been using an iPad as others have suggested. Option 1 is to vecro it to a cabinet or the fridge etc. where it is not in danger of getting caught in a spill. You can navigate just fine with a nuckle or the back of your wrist if your hands are a mess.

Option 2 is put it in a gallon zipper bag. I recommend the 'storage' type over the freezer type as the plastic is thinner and won't interfere with the screen. If you are going to be using it for something with audio it won't sound good, but if you have something with airplay (I use a in the kitchen you can shift the audio over there, which is a good idea anyway as the volume level of an iPad really can't compete with kitchen noise.

I'm considering putting in a permanently mounted 50" LCD screen when I remodel. If so it will be connected to a computer in the basement under the kitchen, and have a touchscreen overlay added to it. The overlay uses light beam interruption and senses 'touch' without you really having to make contact with the screen. This is probably more than most people want to mess with though.