What DIY tools are very critical for plumbing works and repair?
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


Sometimes you just need to get a good grip on a pipe, nothing beats a strap/chain wrench fo this.
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 &amp; 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 &quot;just a quick question&quot;, or want to offer &quot;advice&quot;.