Annual sunflowers grow as ornamentals or they produce edible seeds, while perennials are only grown as ornamentals. Both perennials and annuals come in two main types: single-stem or multibranch. Single-stemmed varieties produce a single large flower atop the main stem, but they may produce smaller flowers lower down on the stem after the main flower wilts. The multibranched varieties have multiple stems, each adorned with at least one flower. These respond best to pinching and deadheading because they are most likely to produce new buds after grooming.
Examples of single-stem varieties include the giant annual sunflower varieties (Helianthus annuus) or the perennial woodland sunflower (Helianthus divaricatus), which is hardy in U.S. Department of Agriculture plant hardiness zones 3 through 8. When growing these varieties for purely ornamental reasons, pinch off the old flower head after it begins to wilt. Pinch above the topmost set of leaves so the smaller flower buds beneath can bloom. Pinch off each of the smaller blooms as they wilt, then cut back the entire plant after it dies back.
Multibranch sunflower varieties benefit the most from regular pinching, with many types reliably flowering for a longer period and producing lusher blooms with frequent grooming. Some annual varieties, such as the aptly named branching sunflower (Helianthus debilis), branch, as do perennials such as the sawtooth sunflower (Helianthus grosse-serratus), which grows in USDA zones 4 through 7. Pinch off the old blooms just above the topmost leaves as they wilt. Continue to pinch off dead flowers at least once a week until the plants naturally stop flowering.
Annual sunflowers grown for seed don't require pinching. Instead, the flowers are allowed to wilt and die completely so the seeds in the center flower disk can fully mature. Cut off these flowers for harvest only after the back of the flower changes from green to yellow or tan. Seed-producing sunflowers won't produce more blooms after you remove the seed head, so you can pull up the entire plant after flower removal.