I was there between 11 and noon today. It was a mob scene to see the impressionists with various groups hogging space in front of major works. Is there a "best" time to visit? There wasn't a long line waiting to get in.
It's open till after 9pm on Thursdays. When I visited in the evening the crowds were very manageable. Also had a great dinner at the museum restaurant.
I saw two restaurants there, but no snack bar, Gone, perhaps.
What Michael said. The Orsay was, by far, less crowded after 5:30 when it's open late. Just like the Louvre. And we really enjoyed dinner in their beautiful restaurant.
We have our tickets in hand and go about 45-60 minutes prior to the opening. We are amongst the first few to enter and we go directly to the top floor to view the impressionists at our leisure. We have been three times over the years and never had a crowd problem by going early. We then work our way down through the rest of the museum and enjoy every part of the Orsay.
If you're looking for Impressionist art, a less crowded alternative is the Marmottan Museum in the 16th arrondisement, on the far side of the Ranelagh Gardens. (About the only disadvantage is that as I remember they are one of the few museums in the city centre that do not accept the Paris Museum Pass.)
To add to what Phillip's said, the Marmottan is for Monet fans. The collection is representative of his works from beginning to end, arranged chronologically with seats for comfortable viewing. I was there in mid-June, around mid-day and there were very few visitors. It's about a 10 minute walk or so from the closest metro station, but pleasant, through a park.
I was just in Paris, and visited the D'Orsay starting at about 2:30 last Thursday. It was a very reasonable time to go. If it were the summer, I'd go later to avoid crowds.The only problem with Thursday is that one of the prime restaurants in the museum is closed.
I also visited Marmottan and enjoyed that, although the directions in the Rick Steves' guidebook are a little vague for getting you exactly there. Yes, it is not covered by MuseumPass, but it will take a credit card if you prefer that. The D'Orsay has many Monets and, IMHO, the ones in the D'Orsay are better than those in the Orangerie or Marmottan. But all three museums are well worth going to.