| Award | Season | |
|---|---|---|
| Golden Globe Award for Best Television Series - Drama (1993) | - | winner |
| Golden Globe Award for Best Television Series - Drama (1994) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1995) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1996) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1997) | - | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1994) | Season 1 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1995) | Season 2 | winner |
| Primetime Emmy Award for Outstanding Drama Series (1996) | Season 3 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1997) | Season 4 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1998) | Season 5 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1999) | Season 6 | shortlisted |