A proper frame-rate independent newtonian physics integration:

    Vector forces = 0.0f;

    // gravity
    forces += down * m_gravityConstant; // 9.8m/s/s on earth

    // left/right movement
    forces += right * m_movementConstant * controlInput; // where input is scaled -1..1

    // add other forces in for taste - usual suspects include air resistence
    // proportional to the square of velocity, against the direction of movement. 
    // this has the effect of capping max speed.

    Vector acceleration = forces / m_massConstant; 
    m_velocity += acceleration * timeStep;
    m_position += velocity * timeStep;

Tweak gravityConstant, movementConstant and massConstant until it feels right. It is an intuitive thing and can take a while to get feeling great. 

It's easy to extend the forces vector to add new gameplay - for instance add a force away from any nearby explosion, or towards black holes.