From my understanding, besides the pipes, I would need the following:
Screwdrivers
Pipe Cutter
Pipe Wrench
Piler
Nut Driver
So, are there other DIY Tools that are missing from my above list that is very critical for my plumbing works and repair?
Best Answer
Wrenches
Pipe Wrench
You'll want at least 2 of these, of different sizes.
Tongue-and-groove pliers
These come in handy all the time, have a few pair at the ready at all times.
Strap/Chain Wrench
Basin Wrench
For those hard to reach places.
Adjustable Spanner
A few adjustable wrenches of various sizes always come in handy.
Tape Measure
You're going to have to measure something, eventually.
Pipe cutters
Copper pipe cutter
Pex/Plastic tubing cutter
Hacksaw
Pipe reamer
You can get ones that do both inside and outside reaming in a single tool. You'l also want a bit of sandpaper.
Pipe Cleaner
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.
Torch
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.
Hammer
Do enough plumbing, and you're going to want to pound something into submission at some point.
Putty knives
You'll need this to scrape gunk off of stuff.
Auger
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.
Penetrating oil
Great for those really stuck joints.
Plumbers putty
You'll need this if you're installing sinks, and/or faucets.
Buckets
You'll always want to have a couple buckets of various sizes on hand.
A Box
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.
Gloves
Leathers
You'll want a good pair of leather gloves, for when you're soldering and doing other knuckle busting types of work.
Rubbers
You'll also want some rubber gloves, for when you've got to touch stuff you'd rather not touch.
Plumbers Crack
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".