You do not need to have a stir plate to make a starter, it just makes it way more efficient allowing a smaller starter to handle what you need. As you do bigger batches, either in volume or gravity you need more yeast (especially for lagers) so having the ability to grow yeast efficiently is desirable.
Currently I don't have a stir plate (though it is under construction, just need a couple parts that I wont have time to get for another week). I oxygenate with O2 at the start then give it a swirl a few times throughout the growth when I get a chance. It works well, but if you follow the guidelines on Mr Malty the volumes needed are just bigger.