| Award | Season | |
|---|---|---|
| Golden Globe Award for Best Television Series - Drama (1981) | - | winner |
| Golden Globe Award for Best Television Series - Drama (1982) | - | winner |
| Golden Globe Award for Best Television Series - Drama (1983) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1984) | - | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1981) | Season 1 | winner |
| Primetime Emmy Award for Outstanding Drama Series (1982) | Season 2 | winner |
| Primetime Emmy Award for Outstanding Drama Series (1983) | Season 3 | winner |
| Primetime Emmy Award for Outstanding Drama Series (1984) | Season 4 | winner |
| Primetime Emmy Award for Outstanding Drama Series (1985) | Season 5 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1986) | Season 6 | shortlisted |