You'll want at least 2 of these, of different sizes.
These come in handy all the time, have a few pair at the ready at all times.
Sometimes you just need to get a good grip on a pipe, nothing beats a strap/chain wrench fo this.
For those hard to reach places.
A few adjustable wrenches of various sizes always come in handy.
You're going to have to measure something, eventually.
Copper pipe cutter
Pex/Plastic tubing cutter
You can get ones that do both inside and outside reaming in a single tool. You'l also want a bit of sandpaper.
Used to clean up the ends of copper pipe before soldering.
Taps and Dies
You might find yourself in a situation where you have to thread some pipe yourself. For this you'll need some Dies, and possiply taps.
Working with copper is likely going to require some soldering, so you'll need a good torch. DIYers usually grab propane, or butane torches. If you've got the extra cash and you'll be doing a bunch of soldering, MAPP torches are what the pros use.
Do enough plumbing, and you're going to want to pound something into submission at some point.
You'll need this to scrape gunk off of stuff.
A great tool for clearing gunked up drains. Either manual or powered, the choice is yours.
Glues, Puttys, and other gunk
PVC primer and cement
You'll need this if you're doing any work with PVC.
Dope and PTFE tape
If you find yourself working with threaded connections, you'll want to have some pipe dope and PTFE tape.
Solder and Flux
When working with copper, you'll probably have to sweat some joints.
Great for those really stuck joints.
You'll need this if you're installing sinks, and/or faucets.
You'll always want to have a couple buckets of various sizes on hand.
The more jobs you do, the more left over fittings and other bits & bobs you'll have. The longer you do plumbing work, the larger the box will have to be.
You'll want a good pair of leather gloves, for when you're soldering and doing other knuckle busting types of work.
You'll also want some rubber gloves, for when you've got to touch stuff you'd rather not touch.
You can't call yourself a plumber, unless your crack is hanging out. It's also great for warding off people who have "just a quick question", or want to offer "advice".