I consider myself part of the human race, as there really isn't such thing as race, considering the there is no great genetic difference (outside of different features coming from living in different climates) between any of the "races". Race is largely a sociological construct used to incorrectly differentiate the different ethnicities. In my opinion, to say that a person from England (of English decent, as in they were Celts living there before the Romans moved in and haven't breed with anyone other than other people of the same background) and a person from say, The Democratic Republic of Congo (same situation as the Englishman) are different races, would be the same as to say that the Englishman and someone from Finland (once again, same idea) are different races, due to the fact that while they both have similar pigmentation, there features would be somewhat different due to different familial traits.
What we do have is ethnicity, which is simply a more narrow, more culture based system of classification.
Fun fact, when the Europeans first went into Africa, thay thought there were four species (what could be called races) in the genus Homo, and that there was a distinct hierarchy. it went as follows
(1) EUROPEANS & OTHER CAUCASIANS
(2) ORIENTAL
(3) BLACKS
(4) ORANGUTANS
Thats right, black people were considered just a step above Orangutans.
To wrap this up, if someone asks, I'll normally tell them I'm of Irish and Finnish decent (though I never say that I'm Irish or Finnish, as that suggests one is actually from those countries, when in reality, my family hasn't actually lived in those countries since before the American Revolution). I don't like to say I'm American to an American simply because it sounds silly to me.