| Award | Season | |
|---|---|---|
| Golden Globe Award for Best Television Series - Drama (1991) | - | winner |
| Primetime Emmy Award for Outstanding Drama Series (1991) | Seasons 1–2 | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1992) | - | winner |
| Primetime Emmy Award for Outstanding Drama Series (1992) | Season 3 | winner |
| Golden Globe Award for Best Television Series - Drama (1993) | - | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1993) | Season 4 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1994) | Season 5 | shortlisted |