I've just worked out an AABB collision algorithm for my 2D game and I was very satisfied until I found out it only works properly with movements of 1 in X and 1 in Y... here it is:

public bool Intersects(Rectanglef rectangle)
{
    return this.Left < rectangle.Right && this.Right > rectangle.Left &&     this.Top < rectangle.Bottom && this.Bottom > rectangle.Top;
}

public bool IntersectsAny(params Rectanglef[] rectangles)
{
    for (int i = 0; i < rectangles.Length; i++)
    {
        if (this.Left < rectangles[i].Right && this.Right > rectangles[i].Left && this.Top < rectangles[i].Bottom && this.Bottom > rectangles[i].Top)
            return true;
    }
    return false;
}

and here is how I use it in the update function of my player :

public void Update(GameTime gameTime)
{
    Rectanglef nextPosX = new Rectanglef(AABB.X, AABB.Y, AABB.Width, AABB.Height);
    Rectanglef nextPosY;
    if (Input.Key(Key.Left))
        nextPosX.X--;
    if (Input.Key(Key.Right))
        nextPosX.X++;
    bool xFree = !nextPosX.IntersectsAny(Boxes.ToArray());
    if (xFree)
        nextPosY = new Rectanglef(nextPosX.X, nextPosX.Y, nextPosX.Width, nextPosX.Height);
    else
        nextPosY = new Rectanglef(AABB.X, AABB.Y, AABB.Width, AABB.Height);
    if (Input.Key(Key.Up))
        nextPosY.Y--;
    if (Input.Key(Key.Down))
        nextPosY.Y++;
    bool yFree = !nextPosY.IntersectsAny(Boxes.ToArray());
    if (yFree)
        AABB = nextPosY;
    else if (xFree)
        AABB = nextPosX;
}

What I'm having trouble with, is a system where I can give float values to my movement and make it so there's a smooth acceleration. Do I have to retrieve the collision rectangle (the rectangle created by the other two colliding)? or should I do some sort of vector and go along this axis until I reach the collision?

Thanks a lot!