I know sight hounds like whippets are normally used for lure coursing but can any breed participate? Are there breeds that it would be best to avoid lure coursing with and if so, why?
According to Wikipedia and the AKC website, only recognised breeds can participate in competition lure coursing trials.
However all breeds as well as mixed breeds can participate in a kind of pass/fail test called the "CAT": Coursing Ability Test (see picture - photograph from J Bagby Photography, reproduced from New AKC Event Allows ALL Dogs to Discover Fun of Lure Coursing). In the CAT the dogs run alone (the photograph was shot at an non AKC event).
The list of breeds allowed to participate in AKC lure coursing trials includes: Afghan Hound, Basenji, Borzoi, Greyhound, Ibizan Hound, Irish Wolfhound, Italian Greyhound, Pharaoh Hound, Portuguese Podengo Pequeno, Rhodesian Ridgeback, Saluki, Scottish Deerhound, Whippet.