Replaced the Theme Tune

A self-explanatory trope. This is exactly what it says on the tin: a show completely replaces its Theme Tune at some point within its run. There are several likely reasons: music licensing issues, an overall change in tone that would make the original theme Soundtrack Dissonance, or just a way of freshening things up if the show is a Long Runner.

Compare Rearrange the Song. Related to Credits Jukebox.

Examples of Replaced the Theme Tune include:

Anime

This is normal for modern anime. Two-cour series will typically get a new OP and/or ED somewhere around episode 13. Longrunners will switch them less frequently. Oddly named sequels will always have new themes.
Death Note had two themes. The first theme was The World, and the second was What's Up, People?!.
Taken to extremes in the second cour of Mawaru Penguindrum where a different end theme was used in almost every episode.
Sailor Moon, after two seasons, changed the singer of the opening song and then, two seasons later, changed the whole song.
Pokémon changes its theme every season.
Yu-Gi-Oh! does this with the Japanese version, but the English dub by 4Kids has two variations of the same theme.
- The English dubs of each subsequent series (GX, 5Ds, and ZEXAL) introduce one new theme song per series, but the same theme is retained throughout a series' run.
Averted with Tokyo Mew Mew.
Over the course of its two-season run, Code Geass changed the opening theme five times. Of note, is the change to third theme - it came after Lelouch accidentally geassed his sister into ordering the genocide of the Japanese & had to kill her to stop it, and was only used for the final two episodes of the first season because of the drastic shift in tone.
Lupin III shifted the opening of each of its series from time to time. The best known example is likely the second series, Shin Lupin III, which used four distinctly different versions of the famous Lupin theme throughout its three-year run.
Gatchaman interestingly replaced its opening theme, with the ending theme (and vice versa) around episode 20. The "new" opening is much better known than the original (which had a children's chorus in a fairly hard-boiled spies and superheroes show).
- There are a few anime that switched the opening theme song with the closing song (and vice versa). It happened with Hakushon Daimao, Hazedon, and Kiteretsu Daihyakka.

Live Action TV

Wheel of Fortune used an Alan Thicke tune called "Big Wheels" until 1983, when it was ousted for "Changing Keys", composed by show creator Merv Griffin. "Changing Keys" was re-orchestrated several times (with Merv having little to no hand in the last two remixes) until the theme was finally retired in 2000 for an unnamed theme by Steve Kaplan. And that theme was retired in 2006 for the current tune, "Happy Wheels" by Frankie Blue and John Hoke.
The Joker's Wild started out with Jean-Jacques Perrey and Gershon Kingsley's "The Savers". Over time, the show changed themes like crazy: a Suspiciously Similar Song version composed by Alan Thicke titled "Joker's Jive", a re-orchestration of "The Savers" by Hal Hidey, a new theme composed by Hidey (which was always the closing theme), and even another Perry and Kingsley song for a very short time. What's more, Barry and Enright also stole the theme from Break the Bank for a tournament of champions.
Lingo used a short, looped "game show"-y music in seasons 1 and 2 (actually a remix of the Dutch verion's theme), and a completely different rock theme from Season 3 onward.
- The complete opposite could be said for the Dutch version. There the "game show"-y tune replaced a rock theme.
The Drew Carey Show. Drew's own "Moon over Parma", "Five O'Clock World" by the Vogues and "Cleveland Rocks" by the Presidents of the United States of America.
The Unit. First "Fired Up", then a different tune by the same guy (perhaps because "Fired Up" was adapted from a Marine Corps cadence and therefore not a good choice for an Army-based show).
In season 4, Big Love changed from "God Only Knows" by The Beach Boys to "Home" by Engineers.
Each season of the S Club 7 TV series had a different song as its opening theme. Miami 7 had "Bring It All Back", LA 7 had "Reach", Hollywood 7 had "You" and Viva S Club had "Alive".
The original V changed its theme tune a number of times during its run.
Auf Wiedersehen, Pet deliberately changed its opening and closing themes for each new series or special.
Space: 1999 got a new composer as part of a general makeover when Fred Frieberger took over as producer in season two.
The Avengers originally had a theme tune by Johnny Dankworth. It also underwent a complete makeover when production was switched from videotape to film, simultaneous with Diana Rigg's arrival, resulting in the more familiar Laurie Johnson theme.
The change of Monk's theme tune is notable as it was implicitly referenced in-show, at a Painting the Fourth Wall monemt.
Babylon 5 made a point of doing this every season, to reflect the changing theme of the show.
Happy Days used "Rock Around the Clock" as its theme tune in its first season, then changed over to a Days of the Week Song specially written for the show.
The Partridge Family: went from "When We're Singing" in season 1 to a similar-sounding but different song, "C'mon, Get Happy".
Chuck went through several incarnations before settling on "Short Skirt Long Jacket".
White Collar has a new theme for season 3.
- Which they changed back to the old theme a few episodes in.
Farscape changed its theme tune between seasons 2 and 3.
The Cosby Show teeters the line of new theme and rearrangement for Season 5 with the orchestral version. It's probably an arrangement because a fragment of the theme is there in two or three places (but much less than the other 7 seasons' intros, which generally followed a 12-bar blues progression).
During its run on ABC, Password changed its set and theme tune for the transition to Password All-Stars. Robert Israel's synthesized theme was replaced by Bob Cobert's "Bicentennial Funk".
Magnum, P.I. had a different theme song for its first year, before switching to the more familar Mike Post arrangement for the second season premire.
Simon and Simon went from a bouncy theme with lyrics from the first season to a more traditionally 80s detective series theme for the rest of the run.
Hardcastle and McCormick started out with the hard pounding theme "Drive". For part of the second season, this was changed to the theme "Back to Back" which emphasized the friendship of the two title characters. "Drive" returned in Season 3.
Remington Steele's first season featured the tune "Laura's Theme" as Stephanie Zimbalist explained the series premise. The second season introduced a theme based on a small bit of incidental music that played as Remington would say something like "God I'm good!" after Laura explained how the case was solved.
Licencing issues forced the removal of the cover version of "My Life" from Bosom Buddies reruns, while certain public domain episodes of The Beverly Hillbillies, Bonanza, The Dick Van Dyke Show and The Andy Griffith Show air on smaller stations without their famous themes.
Boy Meets World had a different Instrumental Theme Tune each season for seasons 1-4. Season 5 introduced a Title Theme Tune that stayed through to the end.
The Nightly Business Report has had four different theme tunes in its 30+ years on air, all were produced by Edd Kalehoff.
Red Dwarf switched from a 2000: A Space Odyssey-style opening theme to an instrumental based off the end credits theme in the third season, as the original theme was too sombre for a sci-fi sitcom. When those seasons were digitally remastered, they had a new opening theme that combined both themes.
The 1998-2004 version of The Hollywood Squares used its own song "I Love Hollywood," sung by none other than Whoopi Goldberg, from 1998-2002. Afterward, it switched to "Hollywood Square Biz," Teena Marie's 1981 single "Square Biz" with new lyrics.
In the first few episodes of Family Matters, the theme song was Louis Armstrong's What A Wonderful World. It was quickly dropped in place for an original theme, As Days Go By.

Professional Wrestling

Both WWE Raw and WWE Smackdown have changed their Real Song Theme Tunes several times over the years.
- Don't forget about the actual wrestlers themselves. This happens all the time due to forming new teams/factions, face/heel turns, etc. As a result it's harder to name someone that DIDN'T change their theme music than it is to name someone that has.

Video Games

The Halo series used a new main theme for Halo: Reach, although the original theme still occasionally appears.
Syphon Filter: Logan's Shadow.
The Time Crisis series replaced its theme for the third installment, then heavily reworked that theme for the fourth.

Western Animation

Garfield and Friends used three theme songs throughout its run — "Friends Are There" for Seasons 1-2, "We're Ready to Party" for Seasons 3-6, and the rap-sounding theme for Season 7. In an interesting variation, "Friends Are There" was sometimes used as a Leitmotif even after its retirement.
Static Shock went through three different theme songs. The first two themes switched back and fourth at times, but the third theme had always played after its debut.
A lot of people may have forgotten (unless they bought the DVDs), but The Flintstones originally had a different title sequence with an instrumental theme tune.
Scooby Doo: The later seasons did away with its iconic "Where Are You?" theme song in its entirety. Many fans assert that this change coincided with an overall drop in the show's quality as it preceeded the introduction of The Original Scrappy by one season.
Johnny Test has had a different theme since its second season.
The Sky Dancers cartoon had a different opening and entirely new background music when it was released in volumes on DVD.