Hitless Hit Album

A very popular album goes gold, platinum, or even double platinum, without containing any hit songs on the singles chart. Songs may appear on genre-specific radio charts, but otherwise the album sells itself.

In The Fifties and The Sixties, albums were often perceived as secondary to hit singles. This began to change when groups like The Beatles and The Beach Boys started to produce albums which tried to avoid Album Filler and make every song count. The British Invasion helped, thanks to the then-common practice of excluding hit singles from albums.

The trope came into its own during the predominance of "album-oriented" rock during the 1970s, when albums making a unified musical statement had become more common. Some Hard Rock and Heavy Metal groups active at this time, such as Led Zeppelin, did their best to avoid releasing singles at all. Similarly, while they did manage to score some hits, the most successful Progressive Rock artists active in this period, including Pink Floyd, Jethro Tull and Yes, were well-known for producing songs which were simply too long to be feasible for release as a single or were much more effective as part of an album.

Also an obvious trend in the career of a Long Runner artist. Consider discography pages on The Other Wiki; album sales are usually consistent or improve with time while hit singles eventually trail off as more airtime is given to new performers.

Alternative Rock

Despite not having an official single, Radiohead's Kid A was their first album to reach number one on the US Billboard 200, and was also number one in the UK, Canada, France, Ireland and New Zealand. Several songs from the album were sent out as promos to radio stations though, and of these, "Optimistic" received enough radio play to get to number 10 on Billboard's Modern Rock Tracks chart.

Country

Jamey Johnson's The Guitar Song went to #1 on Top Country Albums and was certified gold despite two singles stalling out in the 50s and a third only reaching #39. (Keep in mind the country charts only have 60 positions; also, unlike the Hot 100, they're tabulated entirely from radio airplay.) Before that, he went platinum with That Lonesome Song despite "In Color" being the only semi-hit from it.
Pistol Annies, a supergroup comprising Miranda Lambert, Ashley Monroe and Angaleena Presley, got a #1 with their album Hell on Heels even though country radio never touched the single — it got to #55 on the Hot 100 entirely from downloads. Even more impresively, Hell on Heels was a digital-only release until the CD was released in stores a few months later.
Aaron Lewis of alt-rock band Staind went country with the single "Country Boy" from the EP Town Line. The song only got to #87 pop and #55 country (although it also went gold), but the EP was #1 on Top Country Albums.
Extremely common in bluegrass, since it was never really in fashion on country radio. Alison Krauss & Union Station is a prime example, with impressive album sales despite nothing remotely resembling a hit.
- The "Red Dirt" music of Texas is in a similar situation. Many bands and artists spend years, even decades, gaining massive fanbases in Texas, but never strike it big elsewhere. It's to the point where Billboard publishes a separate country singles chart just for Texas.
Nearly everything Ray Stevens released for MCA in the late 1980s. Most notably, I Have Returned (1985) was a #1 on Top Country Albums and went gold despite neither of its singles reaching Top 40 — in an era where a country album going gold was nearly unheard of due to heavily skewed sales charts.

Hip-Hop/Rap

Bone Thugs-n-Harmony had TWO such albums, Btnhresurrection which went platinum, with little to no video or radio airplay. The second one being The Art of War, quadruple platinum and no official hit song.
Wu-Tang Clan: Their first three albums.

Pop

Headquarters by The Monkees debuted at #1 (and then sat at #2 for a very long time after Sgt Pepper came out the next week), despite having no American singles released from it whatsoever, and thus no officially-charting individual songs. "Shades of Gray" and "Randy Scouse Git" have made it as Greatest Hits Album material, though, the latter having been a top-5 single in the UK.
- Sgt. Pepper itself qualifies as an example, as there were no singles released from it in the UK or the US. However, several songs did become popular through radio airplay.
Since coming second in Britains Got Talent, Susan Boyle has enjoyed two albums which have achieved multi-platinum sales worldwide. In America, the first (I Dreamed A Dream) was the best selling album of the year in spite of being released in the fourth quarter. Nonetheless, she didn't get any singles in the Top 40 from either record.
All of Norah Jones' albums have gone platinum, and she has won multiple Grammys, but in the USA only one (her Diamond-selling debut album) has spawned anything that could be called a hit ("Don't Know Why", which only scraped the Top 40).
Before Stunt, Barenaked Ladies' most popular release in the US was the live album Rock Spectacle. It's still considered one of their best albums, but none of the songs on it charted in the US (until "The Old Apartment" was remixed years later).
Saint Dominic's Preview by Van Morrison hit #15 in the US in 1972 even though none of its three singles could manage to crawl past #61.

Progressive Rock

Rush had a couple of these.
Pink Floyd defines this trope. Ummagumma, Atom Heart Mother, Meddle, Obscured by Clouds, Wish You Were Here and Animals. All either gold or (multi-)platinum, none have a US top-100 single. For the first half of their career, Roger Waters certainly seemed to prefer it this way; when "Money" became their first significant hit single in America, he quickly became exhausted of hearing the new fans it won the band yelling for them to play it.

R&B

Janelle Monae's albums have all been on the Top 200 for albums (peaking at 17) but not one of her singles has been in the top 200 singles. This is probably because her albums are all Concept Albums and suffer from Critical Dissonance.

Rock

Marilyn Manson had several albums that were certified either gold or platinum in America, but they've never had a song in the Top 40 and even on the Modern Rock charts they've not had as many hits as other groups with similar popularity. This may be a result of the controversy that they accrued during their peak in the mid-late '90s (especially after the Columbine massacre); radio stations likely didn't want to face boycotts by Moral Guardians for playing "those Satanists" on the air.
Led Zeppelin famously refused to release singles from their albums in the UK, and in America (where they're one of five rock bands to have more than one studio album certified Diamond) they had one Top 10 hit ("Whole Lotta Love") and a handful of releases that just about made it into the Top 40. Like a lot of classic rock groups, their popularity was based on very extensive radio airplay before charts to measure that were widespread.
Metallica's Master Of Puppets did not have any singles released from it, but is one of the most popular and bestselling metal albums ever.

Unsorted

Artists with #1 albums on the Billboard 200 but no top 40 singles on the Billboard Hot 100 include Jill Scott, the Decemberists, Amos Lee, Vampire Weekend, and India Arie.
Fairport Convention's seminal 1969 album "Liege and Lief" effectively invented the British folk-rock movement, although the album peaked at only #17 in the UK and did not contain any breakout singles.
Sony's Super Hits albums are sometimes literal examples. Depending on the artist, the title can be Blatant Lies — most of them seemingly had their 9 or 10 tracks picked by throwing darts at a list of the artist's songs. For instance, Kenny Chesney's Super Hits disc was released in 2007, but the newest song on it is "What I Need to Do" from 2000. The biggest hit on it is the #2 "Me and You" from 1996, and 2 of the tracks weren't even singles.