My favorite icon is the one Rob2 already posted. In USA she is usually called Our Mother of Perpetual Help (OMPH). The Redemptorists are in charge of this icon and promote devotion to her.
She is my favorite because I grew up with her always in the house. For a long time she was the only icon I ever saw because Western Catholic churches in the past haven’t had icons, especially post-Vatican II when they were all getting rid of a lot of old art and old statues etc and making everything “modern” and generic or very plain. The devotion to OMPH was, from what I’ve read, hugely popular in USA during the first half of the 20th century and there were weekly novenas to her everywhere, some of them drawing very large crowds. My mother also grew up with the devotion and she continued to venerate this Mary as an adult, which is why I too grew up with her in our house, in the kitchen right over the sink. (I had to retire that picture of Mary and get a new one because 50 years of Mary getting accidentally splotched with a few drops of water or occasionally falling into the sink or dishpan took their toll, but I’m sure Mary, having been a housewife herself, would understand.)
When I was a child and young teen in the late 60s/ early 70s you could still find OMPH novenas around and we used to go to them. Nowadays they are harder to find, and the most popular Mary novena seems to be the Miraculous Medal Novena (promoted by the Vincentians). But you can still find an OMPH one here and there. Also the Redemptorists had a big anniversary Mass for the image at the National Shrine in DC a few years ago and I went to that.
My second favorite icon is the Panagia of Bethlehem. It’s supposed to be from Russia. I am told it is the only icon of Mary smiling. I have had the lecture on here before about how “icons aren’t supposed to look like actual people” but it’s not hard for me to think that Mary might have actually looked like this.