Personally, I like albums with a 'theme' and even though I too may cut them up or pick favorite tracks, and have made my own recordings of my favorite songs of all my favorite artists before iPod made it so easy, I still really appreciate a theme, and the flow of an album. Of course, most themes are pretty elastic, and it is interesting to see sometimes what someone will include on a themed album.
Some that come to mind:
Gordon Bok's SCHOONERS (one of my Desert Island Disks)
Danny & Geraldine Doyle's EMIGRANT EYES (ditto)
Some old Clancy Brothers (Irish Songs of Drinking and Blackguarding)
any number of old ballad, regional, or sea song albums
Also, when I look at an album, thinking of buying it, I like to see something familiar so I have an idea what sort of thing to expect, and something unfamiliar or what is the point of buying it? I know most performers have songs that are always requested that they would have no interest in recording (like 'The Unicorn' requested of every Irish band) though including one or two of your own 'greatest hits' or most requested would seem a no-brainer, but I certainly have known musicians to skip those and record only the ones no one ever requests because the musician wants to boost those; I think this is an error, and to me it would make more sense to include some favorites to lead the listening audience into the less known or more [sophisticated? arty? varied? who knows what else to add] pieces.
The old LPs or cassettes offered the possibility of one side more 'serious' and one more light; with CDs that does not happen, and while I understand the idea of varying the pacing, occasionally the pacing can vary too abruptly resulting in a jarring sensation.
A really good live performance will often have a pace and flow that lends itself very well to tracks on an album, even a studio album, though as Charley notes, some things don't work as well in the studio as they do on stage. (Others are better in the studio, even if they do not require effects unavailable on stage.)
I also like the track list on the outside of the packaging to indicate more than just the title, for example original songs or instrumentals.
Also, people very often record the songs that are relatively new in the repertoire, whether just written or just added. But it seems to me that often when someone has been performing a song longer, it acquires a depth of interpretation that was not present at the first; I often wish singers would re-record something because I like the current, mature version better than the recorded 'green' version; I expect this applies far more to traditional or tradition-based than pop of course.