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Alternate Recursive Method

The above snippet is equivalent to this, which may better meet your preference:

static int GetGCD(int x, int y)
{
    // If y is equal to 0, return x.
    if (y == 0)
    {
        return x;
    }
    // If y is not equal to 0, recursive call with x as y and y as the remainder.
    else
    {
        return GetGCD(y, x % y);
    }
}

Can also be written as:

static int GetGCD(int x, int y)
{
    // If y is equal to 0, return x.
    if (y == 0)
        return x;
    // If y is not equal to 0, recursive call with x as y and y as the remainder.
    return GetGCD(y, x % y);
}

Depending on your preference.

Iterative Method

There's no need to create tmp every iteration. The variable can be instantiated outside of the loop. Variable swapping can be done in this instance.

static int GetGCD(int x, int y)
{
    int tmp;
    while (y != 0)
    {
        tmp = x % y;
        x = y;
        y = tmp;
    }
    return x;
}

Recursive Method

static int GetGCD(int x, int y)
{
    // If y is equal to 0, return x.
    if (y == 0)
    {
        return x;
    }
    // If y is not equal to 0, recursive call with x as y and y as the remainder.
    else
    {
        return GetGCD(y, x % y);
    }
}

Recursive Method

static int GetGCD(int x, int y)
{
    // If y is equal to 0, return x.
    if (y == 0)
    {
        return x;
    }
    // If y is not equal to 0, recursive call with x as y and y as the remainder.
    else
    {
        return GetGCD(y, x % y);
    }
}

Iterative Method

As stated in other answers, you might use an iterative method:

static int GetGCD(int x, int y)
{
    while (y != 0)
    {
        int tmp = x % y;
        x = y;
        y = tmp;
    }
    return x;
}

There's no need to create tmp every iteration. The variable can be instantiated outside of the loop.

There's no need to create tmp every iteration. The variable can be instantiated outside of the loop. Variable swapping can be done in this instance.