...
    Point direction = new Point(Math.Sign(velocity.X), Math.Sign(velocity.Y));
    Vector2 nextPosition = this.position + velocity;

    Int32 startx = (Int32)((Single)(position.X) / Tile.Size) - 1;
    Int32 endx = (Int32)((Single)(position.X + this.Width) / Tile.Size) + 1;
    Int32 starty = (Int32)((Single)(position.Y) / Tile.Size) - 1;
    Int32 endy = (Int32)((Single)(position.Y + this.Height) / Tile.Size) + 1;

    List<Point> horizontalWall = new List<Point>();
    List<Point> verticalWall = new List<Point>();

    if (direction.X == 1) // moving right
    {
        for (Int32 y = starty + 1; y < endy; y += 1)
            verticalWall.Add(new Point(endx, y));
    }
    else if (direction.X == -1) // moving left
    {
        for (Int32 y = starty + 1; y < endy; y += 1)
            verticalWall.Add(new Point(startx, y));
    }

    if (direction.Y == 1) // moving down
    {
        for (Int32 x = startx + 1; x < endx; x += 1)
            horizontalWall.Add(new Point(x, endy));
    }
    else if (direction.Y == -1) // moving up
    {
        for (Int32 x = startx + 1; x < endx; x += 1)
            horizontalWall.Add(new Point(x, starty));
    }

    foreach (Point point in verticalWall)
        if (realm.TileAt(point.X, point.Y).IsSolid)
        {
            // if our next position would collide with the tile, we fix velocity.
            if (nextPosition.X + this.Width > point.X * Tile.Size &&
                nextPosition.X < point.X * Tile.Size + Tile.Size)
            {
                if (direction.X == 1) // moving right
                {
                    velocity.X = point.X * Tile.Size - (position.X + this.Width) - 0.0001f;
                }
                else if (direction.X == -1) // moving left
                {
                    velocity.X = (point.X * Tile.Size + Tile.Size) - position.X;
                }
            }
            realm.Tiles[point.X, point.Y].Debug = true;
        }

    foreach (Point point in horizontalWall)
        if (realm.TileAt(point.X, point.Y).IsSolid)
        {
            // if our next position would collide with the tile, we fix velocity.
            if (nextPosition.Y + this.Height > point.Y * Tile.Size &&
                nextPosition.Y < point.Y * Tile.Size + Tile.Size)
            {
                if (direction.Y == 1) // moving down
                {
                    velocity.Y = point.Y * Tile.Size - (position.Y + this.Height) - 0.0001f;
                }
                else if (direction.Y == -1) // moving up
                {
                    velocity.Y = (point.Y * Tile.Size + Tile.Size) - position.Y;
                }
            }
            realm.Tiles[point.X, point.Y].Debug = true;
        }
...