I had these in 5th grade and then didn't see them again until I met Andi Keller of daCarbo trumpets. He said, "At the end of each trade show day, I blow a Spitball through each my the demo trumpets. At the end of the week they still look brand new inside."
What are Spitballs? It's a little jar of round sponges in cleaning fluid that you blow through your instrument. Place one Spitball into the receiver, use a pencil to push it past the venturi, press all the valves down, then blow! Often you can catch it on the way out.
I do recommend first that you give your instrument a basic cleaning with a brush, then use Spitballs to keep it in fresh condition.
For euphoniums and tubas, remove the main tuning slide.
Small: trumpet and horn, smaller trombone
Large: larger trombone, euph, tuba
I use these after play testing before I clean and dry the instrument for storage. I've never had one get stuck. If you have... push past the venturi with a pencil or stick, blow harder, and clean your horn with a brush first. :-)