I know of the original Freaky Friday (with a made for TV remake, and a 2003 remake with Jamie Lee Curtis.)
There is Like Father Like Son (1983) with Dudley Moore and Kirk Cameron, Switch with Jimmy Smits, Big, and Being John Malcovich. Then there is The Hot Chick, which probably inspired me to write this thread (I haven't seen it yet.)

Looking on IMDB, there were a few television shows, such as Big John, Little John and Turnabout.
The Acid House has a body-switching segment, and there was a precursor to Switch called Angel on Fire, as well as a TV movie called Hero in the Family. There was also The Mephisto Waltz, A Miracle of Oam and Somwung (Thailand,) Okay Toots! (Charlie Chase,) Rendez-moi ma peau... (France,) Summer Switch (TV Movie,) Tenkosei (Japan,) and X Change.

Does anyone know of any other movies where the mind of one person is in someone else's body, or in their own body at a different age/sex?

18 Again
Vice Versa

Oh, Heavenly Dog with Chevy Chase's brain in Benji's body.

All of Me with Lily Tomlin and Steve Martin in the same body.

Don't forget the mad scientist episode of "Gilligan's Island"!

Honk!

Dream a Little Dream
Quantum Leap (the TV show)
Face/Off
Prelude to a Kiss

Plus there are all the ones where someone dies and comes back in another body, or something similar. Like:
Chances Are
Down to Earth
Fluke
Meet Joe Black

Ghost has a couple of scenes of that.

I know there are others I have seen, I just can't remember any.

Oh, and that Disney Channel show "The Jersey".

The Exorcist?

http://www.allmovie.com/cg/avg.dll?p=avg&sql=CK|26999

1988 18 Again
1991 Age Isn't Everything
1984 All of Me
1988 Big
1989 Dream a Little Dream
1976 Freaky Friday
1958 I Married a Monster from Outer Space
1990 Identity Crisis
1956 Invasion of the Body Snatchers
1978 Invasion of the Body Snatchers
1991 Quantum Leap: Dreams
1991 Quantum Leap: Shock Theater
1990 Quantum Leap: The Leap Home
1940 Turnabout
1947 Vice Versa

At this time, none are available on DVD.

You sure about that?

not sure if it qualifys but shattered with Tom Berenger and Bob Hoskins would be the best by far

Here Comes Mr. Jordan (1941)
Heaven Can Wait (1978)

Also Dead Again

tasha

I forgot Monkeybone...

I can't believe no-one's mentioned the greatest body-switching comedy in the history of ever and then some, Like Vice, Like Versa!



Seriously, if you're a fan of those eighties novelties, then this little film will be ten minutes well spent!



Like Vice, Like Versa! See it now.

There was another that I have been trying to remember the name of. A kid finds a potion in his neighbors RV and him and his friend find that it allows people to switch bodies. After the inevitable accidental switch they confront the neighbor and find out where it came from. When the neighbor was younger he got injured in the desert. Some indians found him and before they helped fix his injuries they switched his body with one of the local indians that had a high threshold for pain and then told him how they did it. The rest of the movie is the whole group driving out to the desert to find the ingrediants to remake the potion and switch everyone back. Can anyone help with the name?

That movie was Like Father, Like Son, which was mentioned in the OP. Like Vice Versa it's a father/son body swap.

While confirming it at IMDB I found this movie called Xchange, based on swapping bodies for instantaneous spacial travel. I've never seen it, but it is an interesting premise.

What about Being John Malkovich? Or Trading Places?

Fallen

How about:

There's an adult film called Chameleons starring Ashlyn Gere, in which this small group of people called "chameleons" (hence the title) has the ability to change into whoever they want for the purpose of sexual exploits. It's actually not too bad of a film, plot-wise.

Dr. Jekyll and Mr. Hyde

Let's not forget Quigley, with a coked out Gary Busey inside a pomeranean.

That's not fair

"Seconds" starring Rock Hudson. Directed by John Frankenheimer(I think).