Fitz Kreiner. Book-only companion, Eighth Doctor Adventures. A singer-songwriter from 1963, his introductory scene has him chatting up an oblivious customer about Lord of the Rings and then pretending to be French for about two pages. He spends most of the novels he's in getting horribly traumatized in various ways (mum killed, brainwashed by Chinese, stranded six hundred years in the future, nabbed by a cult, cloned, shot at...), but tends to keep calm and carry on anyways. And besides, it's always a refreshing change of pace to have a male companion who seems to be head-over-heels for the Doctor. I mean, uh.
Also, there is eventually a bitchy humanoid TARDIS companion. It's that kind of series.
From the main show: I want to pick up Rory and hug him. I might have a small girl-crush on Martha Jones, and really wish she hadn't gotten shafted so badly. Romana is just sort of awesome in every single way. And I love what I've seen of Sarah Jane, but I haven't yet gotten to watch her appearances in the classic series.