It is better to use organic fertilizers for a number of reasons, not the least of which is what you are leaving behind in your environment as you garden.  However, chemical fertilizers can actually damage plants, causing a speed of growth that weakens the plants to disease and damage in the long-term.

Bonemeal:  Promotes strong root growth, use as a base dressing before planting shrubs, fruit, and other perennials.

Plant-based Fertilizers:  Such as comfrey, alfalfa, and soy.  Use to feed vegetables.

Soybean meal:  High-nitrogen source.  Use on annual vegetable beds or as a base dressing in poor soil.

Seaweed meal:  Helps build up humus levels.  Use for annual beds, fruit trees, bushes, lawns.

Rock Phosphate:  Use to correct a phosphate deficiency, good non-animal alternative to bonemeal.

Organic garden potash:  Use to feed fruit and vegetables.

Gypsum:  Supplies calcium without altering PH

If you do need to alter the PH of soil, use ground limestone or dolomitic limestone to make it more alkaline.