What is the size of an enum in C?

An enum is only guaranteed to be large enough to hold int values. The compiler is free to choose the actual type used based on the enumeration constants defined so it can choose a smaller type if it can represent the values you define. If you need enumeration constants that don't fit into an int you will need to use compiler-specific extensions to do so.

Taken from the current C Standard (C99): http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1256.pdf

6.7.2.2 Enumeration specifiers
[...]
Constraints
The expression that defines the value of an enumeration constant shall be an integer constant expression that has a value representable as an int.
[...]
Each enumerated type shall be compatible with char, a signed integer type, or an unsigned integer type. The choice of type is implementation-defined, but shall be capable of representing the values of all the members of the enumeration.

Not that compilers are any good at following the standard, but essentially: If your enum holds anything else than an int, you're in deep "unsupported behavior that may come back biting you in a year or two" territory.

Update: The latest publicly available draft of the C Standard (C11): http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1570.pdf contains the same clauses. Hence, this answer still holds for C11.

While the previous answers are correct, some compilers have options to break the standard and use the smallest type that will contain all values.

Example with GCC (documentation in the GCC Manual):

enum ord {
    FIRST = 1,
    SECOND,
    THIRD
} __attribute__ ((__packed__));
STATIC_ASSERT( sizeof(enum ord) == 1 )