ValueTuple - Update for C# 7

As @cactuaroid mentions in the comments, a value tuple can be used. This saves a few keystrokes and more importantly executes purely on the stack (no Garbage):

(PropA, PropB, PropC, PropD).GetHashCode();

(Note: The original technique using anonymous types seems to create an object on the heap, i.e. garbage, since anonymous types are implemented as classes, though this might be optimized out by the compiler. It would be interesting to benchmark these options, but the tuple option should be superior.)

Anonymous Type (Original Answer)

Microsoft already provides a good generic HashCode generator: Just copy your property/field values to an anonymous type and hash it:

new { PropA, PropB, PropC, PropD }.GetHashCode();

This will work for any number of properties. It does not use boxing. It just uses the algorithm already implemented in the framework for anonymous types.

Using System.HashCode

If you are using .NET Standard 2.1 or above, you can use the System.HashCode struct. On earlier frameworks it is available from the Microsoft.Bcl.HashCode package. There are two methods of using it:

HashCode.Combine

The Combine method can be used to create a hash code, given up to eight objects.

public override int GetHashCode() => HashCode.Combine(this.object1, this.object2);

HashCode.Add

The Add method helps you to deal with collections:

public override int GetHashCode()
{
    var hashCode = new HashCode();
    hashCode.Add(this.object1);
    foreach (var item in this.collection)
    {
        hashCode.Add(item);
    }
    return hashCode.ToHashCode();
}

GetHashCode Made Easy

An alternative to System.HashCode that is super easy to use while still being fast. You can read the full blog post 'GetHashCode Made Easy' for more details and comments.

Usage Example

public class SuperHero
{
    public int Age { get; set; }
    public string Name { get; set; }
    public List<string> Powers { get; set; }

    public override int GetHashCode() =>
        HashCode.Of(this.Name).And(this.Age).AndEach(this.Powers);
}

Implementation

public struct HashCode : IEquatable<HashCode>
{
    private const int EmptyCollectionPrimeNumber = 19;
    private readonly int value;

    private HashCode(int value) => this.value = value;

    public static implicit operator int(HashCode hashCode) => hashCode.value;

    public static bool operator ==(HashCode left, HashCode right) => left.Equals(right);

    public static bool operator !=(HashCode left, HashCode right) => !(left == right);

    public static HashCode Of<T>(T item) => new HashCode(GetHashCode(item));

    public static HashCode OfEach<T>(IEnumerable<T> items) =>
        items == null ? new HashCode(0) : new HashCode(GetHashCode(items, 0));

    public HashCode And<T>(T item) => 
        new HashCode(CombineHashCodes(this.value, GetHashCode(item)));

    public HashCode AndEach<T>(IEnumerable<T> items)
    {
        if (items == null)
        {
            return new HashCode(this.value);
        }

        return new HashCode(GetHashCode(items, this.value));
    }

    public bool Equals(HashCode other) => this.value.Equals(other.value);

    public override bool Equals(object obj)
    {
        if (obj is HashCode)
        {
            return this.Equals((HashCode)obj);
        }

        return false;
    }

    public override int GetHashCode() => this.value.GetHashCode();

    private static int CombineHashCodes(int h1, int h2)
    {
        unchecked
        {
            // Code copied from System.Tuple a good way to combine hashes.
            return ((h1 << 5) + h1) ^ h2;
        }
    }

    private static int GetHashCode<T>(T item) => item?.GetHashCode() ?? 0;

    private static int GetHashCode<T>(IEnumerable<T> items, int startHashCode)
    {
        var temp = startHashCode;

        var enumerator = items.GetEnumerator();
        if (enumerator.MoveNext())
        {
            temp = CombineHashCodes(temp, GetHashCode(enumerator.Current));

            while (enumerator.MoveNext())
            {
                temp = CombineHashCodes(temp, GetHashCode(enumerator.Current));
            }
        }
        else
        {
            temp = CombineHashCodes(temp, EmptyCollectionPrimeNumber);
        }

        return temp;
    }
}

What Makes a Good Algorithm?

Performance

The algorithm that calculates a hash code needs to be fast. A simple algorithm is usually going to be a faster one. One that does not allocate extra memory will also reduce need for garbage collection, which will in turn also improve performance.

In C# hash functions specifically, you often use the unchecked keyword which stops overflow checking to improve performance.