1. New producers entering the market. (More businesses producing a product or service will mean a greater supply of that product or service.)
2. Government taxes and subsidies. (High taxes on a product may discourage suppliers, whereas government subsidies will encourage more of the product to be supplied. A recent example was government subsidy for the production of ethanol, which caused a strong increase in ethanol production and supplies.)
4. Cost of the product or services. (High input costs to provide the product or service will tend to decrease supply, as profit margins for producers are affected.)
5. Future expectation of prices. This one is tricky to call a "non-price determinant," but it's not a current, actual price. It's the anticipation that prices and sales will be strong at some future point. So, for instance, if there is an expectation that flying cars (or personal helicopters) will someday be a high-demand item that will sell for high prices, that will spur development and supply of such an item.
The only one I left out was #3, effect of mass media advertising -- because that is something that is a determinant of demand rather than supply.