Metal Drain Baskets.
These are by far the best drain strainers that I have found which successfully keep stuff, including hair, from making its way down the drain.
They come in small for the vanity, medium for the tub, and large for the kitchen sink. The kitchen sink variety comes with a thin, or a thick ring. I have found that the thick ring for the kitchen sink works best.
I have found them only at flea markets.
They are very inexpensive, costing less than a dollar when bought in sets.