Which Day of the Week was my Birthday?

A short expert note to sit above the replies from @vegaseat and @Lingson: for ordinary modern dates, a standard date library is the safest and simplest choice. Two issues that come up for readers years later are worth calling out: how to handle historical dates (Julian vs Gregorian) and how to compute the weekday if you must do it in plain C without a date library.

Calendar caveats: the Gregorian reform began in 1582 but countries adopted it at different times, so the "local" weekday for a historical date depends on which calendar was in use where and when. If you want a single consistent arithmetic answer instead, use the proleptic Gregorian rules (the Gregorian rules extended backward). Python’s date type is defined that way and documents the supported year range. (docs.python.org)

If a C implementation is required, Zeller’s congruence is compact and reliable for the Gregorian (and has a variant for the Julian) — implement it with the standard month adjustment (count Jan/Feb as months 13/14 of the previous year) and map the result to whatever weekday numbering you prefer. Example (Gregorian case; returns 0 = Monday .. 6 = Sunday):

/* return 0 = Monday .. 6 = Sunday */
int weekday_monday0(int y, int m, int d) {
    if (m < 3) { m += 12; y -= 1; }
    int K = y % 100;
    int J = y / 100;
    int h = (d + (13*(m + 1))/5 + K + K/4 + J/4 + 5*J) % 7; /* h: 0=Saturday */
    return (h + 5) % 7; /* convert to 0=Monday..6=Sunday */
}

Zeller’s derivation, the Gregorian vs Julian variants, and implementation notes are collected in standard references. Test any implementation against a few known anchors (for example the 1582 switch dates and later national switches) so you get the right policy (local calendar vs proleptic) for your use case. (en.wikipedia.org)