- Baby’s tears (Soleirolia soleirolii). Small, dainty creeping leaves form clean, lush green mats with tiny white flowers in summer. Prefers shade and moderate moisture. In colder regions, the plant dies back during winter, but it returns with lush growth as the temperature increases.
- Irish moss (Sagina subulata). Dense tufts of slender stems grow together to form a velvety soft green carpet. Small star-shaped white flowers cover completely in spring.
- Blue star creeper (Isotoma). Forms a flat green ground cover and blooms with pale blue flowers from spring to frost. Easy to grow and maintain.
Check out http://www.stepables.com for ground cover ideas suitable for your needs and climate zone. You can search from 130 varieties of ground covers and lawn substitutes according to plant height, water requirements, flower color, and whether you can walk on it.