Use ordinary cinder blocks (also known as "breeze blocks") embedded with the open sides up, filled with earth and planted with grass. You can still park your car on them, but your driveway will almost disappear.
Renovate existing paved areas such as a patios or garden paths by removing selected pavers and filling the resulting spaces with gravel or plants. Herbs such as creeping thyme are ideal for this purpose, as they are not only functional but also ornamental and edible.
For new areas of paving, use impermeable materials such as flagstones, but separate them widely enough to use permeable substances in between, such as turf, plantings, gravel or organic, biodegradable material like chopped or shredded bark mulch.
Create new paths or areas in dry climates by using natural materials like hardwood stepping 'stones' or four-inch sections sawn from a tree trunk, with the bark removed (it rots more rapidly than the wood itself).
For temporary pathways, use pine straw if it's available. This will interweave with traffic and form a soft, permeable surface that is easily removed.