As far as delegates won in the first 4 contests where delegates were awarded (Iowa, New Hampshire, Nevada and South Carolina), Obama is in the lead. Obama has 63 delegates, Clinton has 48 delegates.
Clinton is in the lead if you count so-called "super-delegates." "Super-delegates" are typically mayors and other prominent public officials (current and retired) who are given this "honor" and theoretically can cast their vote for the candidate of their choosing. Typically, the overwhelming majority of super-delegates wait until the regular delegate process plays itself out, and once the nominee is determined through that process, the super-delegates get on board with the winner. There is no reason to believe the same process will not adhere this time. So far, a tiny fraction of super-delegates have made their selection already (some for Obama, a little more for Clinton), but it is expected that the vast majority of super-delegates will wait and simply go with the winner of the real delegate race.
So, with respect to "delegates" in the normal sense of the word (i.e., awarded based on vote totals in primaries and caucuses), Obama is ahead 63-48. Personally, I don't like it when Obama has the frontrunner mantle because as an African-American running for president against a powerful machine like the Clinton apparatus, I think Barack is always the underdog. But don't get it twisted (and the media will certainly try to twist it), through 4 contests Obama has the most votes and the most delegates.