I give them whatever nickname I think fits (e.g. Exeggcute - Eggy, Delibird - Santa, Politoed - Froggy). I named my favourite Pokemon, Scrafty, after the name I use, Iggy. Also, for some reason, I always call my Fire-type starters "Infernox", and I call any Pokemon that looks like a crocodile "Krox".
EDIT: 2 extra things to add to my post:
1. I did spell Politoed correctly, just in case anyone thinks it's spelt Politoad, which it's not.
2. I don't have a single Pokemon that isn't nicknamed. I used to keep the legendaries' names as they were, with no nicknames, but then I changed my mind.