I actually schedule time to sit down and listen to an album, or double album, in full at least twice a week. My current lifestyle doesn't require I put it in my schedule, but when I was traveling and working pretty much all the time I had to remind myself to stop and relax and do one of the things that makes my life worth living.
I prefer to listen to entire albums - usually on CD if I am at home, but sometimes it is on my phone using my IEMs or over the ear cans. I love the majesty of a good song series which tie together the best the artist(s) could do at that moment and time. I also still find that my favorite song on my most favorite albums tends to shift over time. By isolating the one or two tracks I liked when I first hear a record I miss out on the tracks which may not have appealed to me initially but which grow better and better as I give them more listens. Often the song that ultimately becomes the definitive example of that moment in music making history for that artist(s) isn't the one which stands out on the first few listens, but the one which takes time to understand and appreciate.
But, that's my method. I get deeply engaged emotionally and physically to music, so enjoying the complete collection of songs an artist makes is essential to me.
That said, when it comes to classical music, I listen to the piece I want to hear. Often the signature piece recorded to sell an album isn't long enough to justify a full disc, so the label will ask the orchestra to record something usually by the same composer which goes well with the primary piece. If I put on one of those albums, such as the 1812 Overture, I will only listen to the piece I wanted to hear and not always the entire album which may have some avant garde or modern piece the director imaged would be good for listeners to hear.