If you only use the egg white then you keep a lot of the protein but eliminate the fat in the egg. That's why egg white omelettes are often featured in diet plans.
Omelette with two large eggs and butter: 226 calories, 18.9g fat, 14g protein
Omelette with egg whites from two eggs, no butter: 33 calories, 0g fat, 7g protein
Other sources of low fat protein include:
grilled chicken breast, no skin (3.1g fat per serving - half a breast)
tofu (4.1g fat per serving)
chickpeas (2.2g of fat per cup)
cottage cheese (2.4g per serving - half a cup)
However bear in mind that you get less protein per serving from the vegetable sources, so while you're saving in fat you're also lowering your protein.
And don't forget fish:
tuna tinned in brine (2.2g fat per serving)
Some types of fish, like salmon, are higher in fat than skinless chicken breast but fatty fishes contains healthy omega 3 fats which are very good for you. You need a little fat in your diet anyway so it's best to make it as healthy as possible.
You can also add protein to your diet in the form of whey powder in your smoothies. It is high in protein but incredibly low in fat. That's why it's favoured as a protein source by body builders.