As of today these are the top ten favorites:
THE TRIP PART 2...Season 4...9.2 rating
THE COUNSELOR...S4...8.9 rating
THE SPELLING BEE...S3...8.8 rating
JOBLESS...S3...8.7 rating
VALENTINE'S DAY...S2...8.6 rating
THE TICKET...S3...8.6 rating
THE COMPETITION...S3...8.6 rating
THE CADET...S3...8.6 rating
STRANGER IN THE NIGHT...S1...8.2 rating
THE OUTCASTS...S1...8.0 rating and THE FIELD...S6...8.0 rating (tie)
The rankings have changed slightly in the past few days:
1. THE TRIP PART 2...Season 4...9.2 rating
2. THE SPELLING BEE...S3...8.8 rating (up from #3)
3. JOBLESS...S3...8.7 rating (up from #4)
4. THE COUNSELOR...S4...8.6 rating (down from #2)
5. VALENTINE'S DAY...S2...8.6 rating
6. THE TICKET...S3...8.6 rating
7. THE COMPETITION...S3...8.6 rating
8. THE CADET...S3...8.6 rating
9. THE APARTMENT...S4...8.4 rating (debuts on the list)
10. STRANGER IN THE NIGHT...S1...8.2 rating (down from #9)
It's been over a month since I updated this, and these results come after Antenna-TV's first full run of the show:
1. THE TRIP PART 2...Season 4...9.2 rating
2. HEATHER'S TUTOR...Season 2...9.0 rating (debuts on the list)
3. THE COMPETITION...Season 3...8.8 rating (up from #7)
THE SPELLING BEE...Season 3...8.8 rating (down from #2)
PAPER MILL...Season 6...8.8 rating (debut)
THE COUNSELOR...S4...8.6 rating (up from #4)
7. JOBLESS...Season 3...8.7 rating (down from #3)
FEAR OF FLYING...Season 6...8.7 rating (debut)
9. VALENTINE'S DAY...Season 2...8.6 rating (down from #5)
10. THE TICKET...Season 3...8.6 rating (down from #6)
DEPORTATION PT 1...Season 3...8.6 rating (debut)
It's about a year later, and I thought it would be interesting to see how the rankings have changed. The Trip Part 2 is still the top rated episode here on the IMDb:
4.14 The Trip: Part 2
4.18 The Apartment
5.6 Duel
2.19 Heather’s Tutor
3.14 The Ticket
2.17 The Will
4.16 Heather’s Monk
4.20 The Counselor
3.9 The Spelling Bee
3.13 Jobless
Time for an update:
4.14 The Trip: Part 2
4.18 The Apartment
4.16 Heather's Monk
6.8 Fixed
5.6 Duel
2.17 The Will
4.8 Christmas Story
4.19 Graduation
2.19 Heather's Tutor
3.9 The Spelling Bee
During the original run, the highest rated episodes (in terms of viewership, of course) were the Pilot (watched by 17.2 households; typically, the Pilot for any new TV show is the most-watched episode) and "Sweet Charity" (watched by 16.1 households).
https://en.wikipedia.org/wiki/List_of_Mr._Belvedere_episodes
As you can see, ratings were fairly decent. Despite not being in the top 30, it did well enough against its Spring-replacement competitors on CBS and NBC to be picked up for a full season that fall. They did take a bit of a nosedive with the season 3 premiere, and I guess that was what prompted ABC to cancel the program after the season ended, but the biggest nosedive came with the timeslot change in season 6.