I am looking for the title of a science fiction movie that I saw
several times between 1990 and 1998.  Much of it takes place on a
large spaceship and on the surface of a dangerous planet.  A scene I
remember well takes place on the spaceship in the workout room- the
crew had small black bands in their hands with which they could set an
amount of resistance to use for weightlifting.  Later, a crew member
is accidently(?) sucked out of the ship- foul play was likely afoot. 
Later the crew ends up on a planet where they are locked in suspended
cages.  The crew leader then engages in a battle to the death around a
pit of fire or lava.  Any sci-fi fans able to help?

I believe you're remembering Disney's "Earth Star Voyager," which was
first shown in 1988 and had been aired several times since. It was
intended as the pilot for a TV series, but the series never happened.
"Earth Star Voyager" has the adjustable hand-weights that you've
described, and also features a climactic battle between the good guy
and the evil guy over a vortex or a volcano or a magma whirlpool or
something equally dangerous (my memory is a bit foggy after all these
years).

Here are a few plot summaries:

"The Earth's Atmosphere has become Acidic and polluted over the years,
regardless of what's been done to help it. Space probes have returned
information about a Class M planet, Dimiter, that humans may be able
to inhabit. The most intelligent teenage military minds have been put
together in a 25 year round trip mission to check out the planet and
return with the information. In transit they come up against elder
leaders who have swayed their position to universal takeover by
including the youth piloted transport as their military flagship and
the firstlings of a supreme race. The plot unfolds as members of the
crew realize there are spys and sabateurs on board, eliminating key
people that could prevent the hidden master plan. A wild joker in the
deck, from a previously space-pirated ship, joins the crew to help
keep the return mission on the intended course to Dimiter, and back."

Movie Tome: Earth Star Voyager
http://www.movietome.com/movietome/servlet/MovieMain/movieid-1427/Earth_Star_Voyager/

"The year is 2088. Decades of pollutants, erosion and neglect have
made a wasteland of Planet Earth. Now its inhabitants are forced to
look for shelter in another solar system. A youthful crew of
scientists is recruited to find a habitable planet to save the human
race from extinction. Aboard their inter-galactic spaceship,
'Earth*Star Voyager', they embark on an incredible 26 year quest where
they encounter strange and deadly lifeforms, as well as treachery
among their own crew members."

SendIt: Earth Star Voyager
http://www.sendit.com/video/item/7000000003935

"There was a spaceship piloted by a group of children/teenagers
looking for a new planet to colonize...  Their propulsion system was
called the slingshot drive... One of the male children is in the gym
working out, however the weights that he is bench pressing is replaced
by small plate like device that simulate weight on the palm of his
hands (which would normally be where the barbell was)."

Post from rec.arts.tv newsgroup
http://groups.google.com/group/rec.arts.tv/msg/fc1b6252911ffbd9?dmode=source&hl=en 

Here you can see several photos of miniature space ships that were
used in "Earth Star Voyager":

JetCafe: TV Movies and Series #2
http://www.jetcafe.org/bruce/portfolio/TV_Shows2/

As far as I know, "Earth Star Voyager" has never been released as a
commercial video. Bootleg copies occasionally show up on eBay and in
newsgroups.

My Google search strategy:

Google Web Search: "earth star voyager" OR "earthstar voyager"
://www.google.com/search?hl=en&q=%22earth+star+voyager%22+OR+%22earthstar+voyager%22

I hope this is the correct movie. If it is not, or if anything is
unclear or incomplete, please request clarification; I'll be glad to
offer further assistance before you rate my answer.

Best regards,
pinkfreud

Well done- and to anyone who stumbles upon this in the future:

This seems to be the best place to get a copy:
http://www.geocities.com/hollywood/hills/1742/

Although you can also purchase one from here:
http://www.ioffer.com/bi/sgeti--Earth-Star-Voyager-DVD-NTSC-Full-Version--1.1-2.10-9491490

I seem to recall something like this from the early '90s. The movie I
saw was on The World Of Disney, on a Sunday evening, and it definitely
had a scene in the fitness center with the personally adjustable hand
weights. The story had a crew onboard a starship which was propelled
by a sci-fi type stardrive, which was analogous to the spaceship being
drawn along on an extremely long rubber band through space. I don't
remember the title. Was there also a scene in which they improvised a
weapon (a cannon) out of an electromagnetic mass driver?

I think you are right: it was a Disney movie.  I also recall a
teenager in the movie and some kind of love interest with a girl on
board.  I don't specifically remember the cannon/weapon.  Thanks for
the comment- I'm trying to identify and purchase it by Christmas!