Scotch moss stay evergreen in winter and feature small white flowers in late spring. In our sunny climate, Sagina subulata requires some shade and water to thrive. In contrast, thyme is great for those hot, sunny areas and boasts marvelous fragrance. Thyme flowers are pink or lavender in summer. Blue varieties often keep better color if they are planted in shadier sites.
Many ground covers, like most perennial plants, only flower for a month or two in spring or summer.
If not, maybe you should consider one of the more prostrate varieties of dianthus. Dianthus deltoides 'Brilliant' and 'Zing Rose' feature rosy red flowers in May and June followed by deep green mat-like foliage, while Dianthus grantianopolitanus 'Firewitch' is a happy combination of neon pink flowers and short, powdery blue foliage. If you love true blue flowers, plant one of the many varieties of creeping veronica. Finally, as you shop the wonderful world of ground covers, calculate how much time you want to spend caring for your plants. Although many ground covers are low maintenance, no ground cover is no-maintenance.