The old 32-bit registers have been extended to 64 bits, the r registers (rax, rbx, rsp and so on).
In addition, there's some extra general purpose registers r8 through r15 which can also be accessed as (for example) r8d, r8w and r8b (the lower 32-bit double-word, 16-bit word and 8-bit byte respectively).
The high byte of the old 16-bit registers is still accessible as ah, bh, and so on, but this appears to not be the case for the r8 through r15 registers.
In addition, there's some new SSE registers, xmm8 though xmm15.
The eip and flags registers have also been extended to rip and rflags.
See the wikipedia page and MSDN for more details.
Whether these are supported in the asm keyword for a particular C compiler, I couldn't say. What little assembly I do (and it's becoming about one day a year) is done in assembly rather than C.