Player.cs

using Microsoft.Xna.Framework;
using Microsoft.Xna.Framework.Input;
using Microsoft.Xna.Framework.Graphics;

public class Player
{
    public Rectangle Bounds
        => new Rectangle((int)_pos.X, (int)_pos.Y, 16, 16);

    Vector2 _prevPos;
    Vector2 _pos;
    Vector2 _vel;

    World _world;

    const float GRAVITY = 500;
    const float MOVE_SPEED = 100;
    const float JUMP_FORCE = 275;
    const float MAX_FALL_SPEED = 350;

    public Player(Vector2 position)
    {
        _pos = position;
        _world = Main.World;
    }

    public void Update(float dt)
    {
        // Gravity
        _vel.Y += GRAVITY * dt;
        _vel.Y = MathHelper.Clamp(_vel.Y, -MAX_FALL_SPEED, MAX_FALL_SPEED);

        // Horizontal movement
        if (Input.IsKeyHeld(Keys.A))
            _vel.X = -MOVE_SPEED;
        else if (Input.IsKeyHeld(Keys.D))
            _vel.X = MOVE_SPEED;
        else
            _vel.X = 0f;

        // Jumping
        if (Input.IsKeyDown(Keys.Space))
            _vel.Y = -JUMP_FORCE;

        // Calculate position
        _prevPos = _pos;
        _pos += _vel * dt;

        HandleCollisions();

        System.Console.WriteLine("Velocity: {0}", _vel);
    }

    void HandleCollisions()
    {
        Rectangle bounds = Bounds;
        Rectangle prevBounds = new Rectangle((int)_prevPos.X, (int)_prevPos.Y, bounds.Width, bounds.Height);

        // Only check blocks around player
        int left = bounds.Left / TileData.TILE_SIZE;
        int right = bounds.Right / TileData.TILE_SIZE;
        int top = bounds.Top / TileData.TILE_SIZE;
        int bottom = bounds.Bottom / TileData.TILE_SIZE;

        for (int x = left; x <= right; x++)
        {
            for (int y = top; y <= bottom; y++)
            {
                // Not a solid block
                if (_world.GetBlock(x, y) == -1)
                    continue;

                Rectangle blockBounds = new Rectangle(x * TileData.TILE_SIZE, y * TileData.TILE_SIZE, TileData.TILE_SIZE, TileData.TILE_SIZE);

                // Resolve collision on x axis
                if (bounds.Intersects(blockBounds))
                {
                    // Previously to left of block
                    if (prevBounds.Right <= blockBounds.Left)
                    {
                        _pos.X = blockBounds.Left - bounds.Width;
                        _vel.X = 0f;
                    }
                    // Previoulsy to right of block
                    else if (prevBounds.Left >= blockBounds.Right)
                    {
                        _pos.X = blockBounds.Right;
                        _vel.X = 0f;
                    }
                }

                // Perform further collision using new bounds
                bounds = Bounds;

                // Resolve collision on y axis
                if (bounds.Intersects(blockBounds))
                {
                    // Previously above block
                    if (prevBounds.Bottom <= blockBounds.Top)
                    {
                        _pos.Y = blockBounds.Top - bounds.Height;
                        _vel.Y = 0f;

                        // _isGrounded = true; Doesn't work due to float and int mismatch
                    }
                    // Previoulsy below block
                    else if (prevBounds.Top >= blockBounds.Bottom)
                    {
                        _pos.Y = blockBounds.Bottom;
                        _vel.Y = 0f;
                    }
                }
            }
        }
    }

    public void Draw(SpriteBatch spriteBatch)
    {
        spriteBatch.FillRectangle(Bounds, Color.White);
    }
}