Many shows have broad appeal, and most people who see them generally have a positive or neutral opinion on their value. Others appeal to a niche market and get positive views from their target audiences, while mainstream viewers are merely indifferent. Others are awful, but a lucky few of those manage to gain fans who like them because they're so bad.
Some, however, manage to achieve the result of intensely polarizing viewership, with the result that nobody thinks the show is average or "worth watching, if there's nothing else on". Half of the viewers laud the series as the greatest, most intelligent, engaging thing ever to grace the small screen, and the other half condemning it as a horrible, worthless load of festering bollocks that clutters the airwaves with reeking lines of awfulness.
Similarly, with Video Games and albums, reviews take the form of either "This is the best game/album ever - buy it now!" and "This game/album should never have been made. Avoid."
Sequels or remakes to existing properties that significantly change the source material are particularly prone to this kind of reception. People tend to either love the work as a reinvention/evolution of the source material, or despise it for changing too much and/or losing the spirit of the beloved original.
When this happens within a fandom, it's known as Broken Base. Serious Business tends to aggravate the problem. Expect various forms of Take a Third Option, though this usually ends up being just a third point of extremes.
See also Hype Aversion, Hype Backlash, Confirmation Bias, Contested Sequel. Applied to food and drink (and fierce poison), this is usually Foreign Queasine. May form a Hatedom. Compare Base-Breaking Character, which is basically this trope when applied to characters. A Ban on Politics is in effect on many discussion forums to avoid such controversial topics.
- Exploited in ads for Marmite. The manufacturers use "You Either Love It or Hate It" as their advertising slogan, giving this trope an alternative name: The Marmite Effect. As David Mitchell pointed out, this works by creating a False Dichotomy: If you don't hate it, you must be one of those people who loves it, so why haven't you got any in the house?
- Used in a series of ads for Miracle Whip salad dressing — different folks talking to the camera about how they love it or find it vile.
- In Bleach: Fan Works, a collection of fictional authors posting fanfics about Bleach, the typical reaction by the readers (both fellow authors, Bleach characters, and others) is to either gush over them or write an utterly scathing review pointing out the many flaws and inaccuracies contained within.
- Neal Shusterman's Scorpion Shards has a character cursed In-Universe with Love It or Hate It. Every woman he meets immediately falls madly in love with him, and every man he meets immediately develops a powerful and Irrational Hatred towards him. Oh, and if he actually kisses a girl, his curse sucks her soul out of her body somehow. Tough break. (It turns out his true superpowers are more benevolent, but he's been corrupted by an otherworldly power-sucking parasite.)
- Discussed and then deconstructed in one of the books of Marc-Uwe Kling with regards to Nickelback
- Marvin the Paranoid Android from The Hitchhiker's Guide to the Galaxy is philosophical about it:
Life... hate it or ignore it, you just can't like it.
- Mother 3 has the Peculiar Cheese item. How much HP is restored from it depends on who eats it. Those who love it regain more HP, and those who hate it regain less HP.
- Played with in Metal Gear Solid 3: The more Snake eats items he doesn't like, the more stamina he regains and the more he starts to enjoy them. However, he loves ALL the items that give you full stamina.
- The yearly Interactive Fiction Competition has a special award for games that fall into this category: the Golden Banana of Discord, given to the title with the highest standard deviation.
- The person who started the Email Discussions thread on Worst and Best Christmas Music reckoned that many songs would end up on both lists. Which of course is what happened.
- South Park spoofed the critical and popular reception to Indiana Jones and the Kingdom of the Crystal Skull. Much of the town seems to hate it - to the point that they consider it nothing less than a crime against humanity - but a small and scattered part of the town, including Butters, really enjoyed it.