Textual Celebrity Resemblance

Creating new characters and describing them in detail so the reader has a quick and easy understanding of what they look and sound like is tough. Much easier? Describing them as looking or sounding like a famous celebrity! If the reader knows the celebrity (and that might be a big if, depending on target audience and the amount of time that passed since the work was published), it allows for a quick reference and something the reader can picture quickly. If not, then the reader is cheated out of a description in what might seem like lazy shorthand.

Common in Fan Fiction by less ambitious authors. Why bother wasting words on descriptions when you can just say your heroine looks just like Cameron Diaz or Audrey Hepburn?

Note: This is a narration in literature trope. Please don't add any examples that exclusively involve dialog or internal monologue. This refers only to when the narration of the story itself describes characters' appearance by making a celebrity comparison, not when characters do.

Contrast with plain ol' Celebrity Resemblance.

Examples of Textual Celebrity Resemblance include:

Fan Works

Ebony opens the notoriously bad Harry Potter fanfiction My Immortal by describing herself as looking like Amy Lee, and states that anyone who doesn't know who she is should GTFO. Other characters (despite them, being featured in a hit movie, having their actors be celebrities) also are described as resembling celebrities, such as Vampire Potter and Joel Madden, or Draco Malfoy and Gerard Way.

Literature

Left Behind describes its villain, Nicolae Carpathia, as looking like a young Robert Redford. This is meant to give an idea of the charm he evokes. In one book, the female lead was established as having a crush on Robert Redford, and the male lead was described as looking a bit like him "if he was a rummy and a drunk." This is clarified within the same paragraph as like "two people had constructed a model human from identical parts, but one had followed the instructions and the other had just bashed it together."
In X-Men novels, Storm is now described as resembling Halle Berry.

In the Sweet Valley High books, Mr. Collins was described as looking like Robert Redford. In the new, updated editions he's just described as looking like "a movie star".
Parodied in So Long And Thanks For All The Fish:

If you took a couple of David Bowies and stuck one of the David Bowies on the top of the other David Bowie, then attached another David Bowie to the end of each of the arms of the upper of the first two David Bowies and wrapped the whole business up in a dirty beach robe you would then have something which didn't exactly look like John Watson, but which those who knew him would find hauntingly familiar.

In the last book of Robert Rankin's Armageddon: The Musical trilogy, a group of minor characters with No Fourth Wall insist that, since Rankin never bothered to describe them, they can decide they all look like celebrities.
Major Major Major Major in Catch-22 is described as looking so much like Henry Fonda that some of the other characters even start to suspect that he is Henry Fonda. In an interview, Joseph Heller said that, in a movie version, he would want Major to be played by either "Henry Fonda or by somebody who looks nothing like Henry Fonda." (In the 1970 film adaptation, he was played by Bob Newhart).
How Not to Write A Novel marks this as a lazy and ineffective storytelling device.
John Dies at the End has a lot of fun with this. For example, there's a cop the narrator describes as looking like Samuel L Jackson, so that's what he's referred to as for the rest of the novel. It then subverts this by having a character named Jennifer Lopez who looks nothing like the singer.
In Ian Fleming's first James Bond novel (Casino Royale), 007 is described as looking like Hoagy Carmichael.
Mark Renton of Trainspotting (the book, not the film) is said to resemble Alex Mcleish.
Eccentric Millionaire Hubertus Bigend, the titular character of William Gibson's Bigend Books, is described as looking "like Tom Cruise on a diet of virgins' blood and truffled chocolates".

Video Games

Many MUSHes will allow players to set actors for their characters (often referred to as PBs, for "played by").