Bill Nighy is somewhat like Christopher Walken in that they both have a quite parody-friendly collection of tics and mannerisms. Unlike Walken though, Nighy seems more capable of rising above his twitchiness to create credible and moving characters. In the clip below, one can see his prototypical moves: a man distracted by himself and his thoughts.
What I find profound about Nighy (and quite a few other British actors, and this might say more about the acting styles across the pond than about him) is that he actually appears to think before speaking. There is much more unspoken dialogue than the quick machine like repartee we are used to in most films and televisions.
Recommended highly are Girl in the Cafe, a profoundly moving few days in a tender yet uncomfortable (for him) relationship amidst his participation at a G8 summit. Opposite him is the wonderfully Scottish Kelly Macdonald.
Apologies for the low quality but I think it gets the point across. The sound comes in at 2:45, just in time to fill in one of the great first meeting scenes in cinema. Though television (and perhaps good television is now surpassing film?) this is a great film, every scene a keeper.
Also, from a few years before, with the both of them is a brilliant piece of television called State of Play (much superior to the American film based on it).