Speaking of Bewitched not having the lyrics sung in its opening theme, (Lyrics are sung in the Bewitched movie) there are other shows that the lyrics aren't sung, or there are extended versions (more verses).

The Dick Van Dyke Show: Never had lyrics in its theme, but in later years, Dick Van Dyke along with backup singers sang the song's lyrics, Barbershop quartet style, on The TV Land Awards.

TheThat Girl theme never had lyrics, until the final season.

All in the Family's theme, Those Were The Days, has more verses.

Cheers theme, has more verses, that was a hit song in the early '80's.

Desi Arnaz sings the lyrics to the I Love Lucy theme at the his club.

The "I Dream Of Jeannie" theme song had lyrics that were never used on the show.

The M*A*S*H theme had lyrics that were never used in the show.

The M*A*S*H theme had lyrics that were never used in the show.
I was just thinking of that. The lyrics were used in the motion picture. The lyrics "Suicide is Painless" was probably considered to dreary for a sit-com/drama.

"The Andy Griffith Show" theme has lyrics that weren't used on the show since they opted to go with a whistled version.

"THE BEVERLY HILLBILLIES" theme ("THE BALLAD OF JED CLAMMPET") had a second verse that was never sung on the show. Same with the "PETTICOAT JUNCTION" theme.
"THE ODD COUPLE" theme had words.
The "STAR TREK" theme had words.
The theme for "THE MUNSTERS" had words.
The "LEAVE IT TO BEAVER" theme had words.

"The Andy Griffith Show" theme has lyrics that weren't used on the show since they opted to go with a whistled version.

The lyrics were written by character actor Everett Sloane who starred as Jubal Foster in "Keeper of the Flame."

Speaking of Bewitched not having the lyrics sung in its opening theme, (Lyrics are sung in the Bewitched movie) there are other shows that the lyrics aren't sung, or there are extended versions (more verses).

The Dick Van Dyke Show: Never had lyrics in its theme, but in later years, Dick Van Dyke along with backup singers sang the song's lyrics, Barbershop quartet style, on The TV Land Awards.

TheThat Girl theme never had lyrics, until the final season.

All in the Family's theme, Those Were The Days, has more verses.

Cheers theme, has more verses, that was a hit song in the early '80's.

Desi Arnaz sings the lyrics to the I Love Lucy theme at the his club.
on the season 4 set of "THE DICK VAN DYKE SHOW" there's a clip of him singing the theme at a show in hollywood in, I think, 2003.

Mama's Family, even though Vicki Lawrence had written some lyrics for it.

Also the following TV themes had lyrics:

Bonanza
My Favorite Martian
Rin Tin Tin
Wagon Train

Cheers theme, has more verses, that was a hit song in the early '80's.

It only hit #83 on the Top 100 pop chart. I've never heard the radio play it. What made it a hit?

The radio versions of the theme songs for Happy Days and Laverne and Shirley were longer than their TV show counterparts.

Sitcoms:

All in the Family's closing theme "Remembering You" I think had lyrics never heard on the air, although there was a clip somewhere of someone singing lyrics to that song.

Designing Women - up until the last few seasons, the theme was always some type of instrumental version of "Georgia On My Mind."



Non-sitcoms:

Baretta - originally didn't have the lyrics until the start of that show's 2nd season.

One Life to Live (1980s-very early '90s) - originally had 2 instrumental versions: one was used during December 17-28, 1984, then a re-orchestrated version used from December 31, 1984 until sometime in 1986 for the opening credits, which occasionally alternated with the lyrical version, based on Peabo Bryson's fall 1985 episode appearance that was used in the closing credits from late 1985 until very late 1991.

The lyrical version was used in the opening credits in early 1986 until OLtL changed their opening credits in very early 1992.

Young and the Restless - in one the closing credits of one 1975 episode, they had the usual theme song...played with lyrics.