When done right, I do think a good "concept" does help an album. You can enjoy the individual tracks, but with some sort of "concept" they can add up to even more than the sum of the parts.
Pink Floyd goes near the top of the list -- they didn't invent it but got more mileage out of "the concept" than anyone else. Though by "The Wall" I think it got out of hand (Waters' desire to be Conceptmeister killed off the group chemistry that made them great.)
Magma is mind-blowing, doubly so because they made up their own language thus their albums work based on "pure music" and the listener has to make up their own "dialogue" as it were. I have a crazy hunch "MDK" will be one of the most listened to works of the 20th century 100 years from now.
I tend to like concept albums that are "cohesive without being narrative." For example KISS "Dressed To Kill" and "Rock And Rollover" are better concept albums than "The Elder" . . . !
Always thought "Tommy" was a solid composition, but poorly recorded and boring as an album (live versions tend to be shorter & punchier). I prefer "Who's Next" as concepts go (remnants from a rock opera that still hang together thematically without the boring "plot and characters" to weigh things down.)
Never been able to get into "2112" or "Lamb Lies Down" for some reason. The latter seems like it should be right up my alley (the concept is so loose it's more like a puzzle than a story) -- I like puzzles (and pretentiousness!) But the music has never intrigued me as much as the album art and liner notes.
Zappa did a bunch, "Absolutely Free" and "Money" hang together quite well I think.
Neil Young "Trans" and "Tonights The Night" seem like his most conceptual from the old days, though I really like "Greendale" and offer that as the exception where I think the overly-narrative approach is actually a major strength. (Neil's dad was a famous novelist in Canada, I think this was Neil's attempt to do his own version of "a novel"! A terrible idea which shouldn't work, but miraculously does in this case.)