If your cabinets are framed, 1/2" plywood is fine for the sides and bottoms. If frameless, 5/8" or thicker material is more desirable.

At some risk of being shot, there are popular framed lines using 3/8" sides and its not considered a quality method of construction. Either type sometimes is made with 1/4" bottoms - also not considered quality.

1/4" thick backs are used a lot. Its mostly dust protection, not a structural piece. A lot of older quality cabinets that were built on site have nothing. A good quality cabinet will have the back loose in a channel cut into the side wall and bottom. Its cool because it lets the relatively big piece expand and contract without ripping the cabinet apart by its fasteners. Lesser stuff will have the back nailed on or attached primarily with hot glue.

There will also be a structural 1/2"-3/4" hanging rail to screw through when attaching the cabinets to the wall - 2 for upper cabinets and a single for lowers. Sometimes, the hanging rail is behind the plywood and sometimes in front.

Drawer bottoms are ok at 1/4" unless you plan to store your 125 silver service or your collection of cast iron trivets in a small drawer. 1/2" drawer bottoms in a mortise and tenon drawer box sounds a little strong (3/8" is more typical), but i wonder if that's just more economical to stock only a few depths of plywood? A best quality drawer would have a loose bottom contained in channels that rim the drawer sides. Long lasting drawers have also been made using 1/2" ply for the sides and bottom and put together with appropriate fasteners through everything or with metal boxes (blum makes some).
HTH

3/4" plywood will make a quality and long lasting cabinet. Is it required? Not necessarily. How the cabinet is put together is a factor as well as the fastners and the adhesives used.
My personal preference is to use 3/4 inch veneer core plywood, but if the customer wants something else, as long as they pay for it, they get what they want.
There are many reasons to use 3/4" but they main reason that thinner material is used is related to cost. Will the thinner material stand up? In many cases it has. Lots of factors to consider. Length of service, countertop material, environment are just a few. Again is mostly what you personally feel comfortable with.

I forgot, ask dude to show you a cabinet that is not installed. Turn the cabinet around and look at the top, back and bottom carefully. It needn't look finished, but it should look neat and tidy.

Hot glue and staples are the devil's playthings.

1/2" ply on framed cabinetry is fine. A common option on semi-custom is to get a flush side on the exposed ends of cabinets. This will get you the 3/4" side where it matters, 1/2" everywhere else.

I built my own frameless cabs.
This is what I chose because of availability of materials, familiarity with building techniques and other reasons

- Sides, tops and bottoms 3/4" prefinished birch ply
- Shelves, 3/4" pre bir ply
- backs and drawer bottoms 1/4" pre bir ply
- drawer sides 3/4" pre solid birch
- doors and drawer fronts - 3/4" solid red birch

I am very happy with how it all turned out. I prefer to make integrated cabinet tops rather than have a separate plywood support for countertops

1/2" plywood would have worked too but i couldnt find it in prefinished.

Thanks for this feedback, I appreciate it. The cabinetry we are looking at is inset. Does that have any impact?

Yes - it sure does. The primary driving factory on cabinet pricing is door style. Inset doors are typically at the top tier in regards to pricing in most cabinet lines.

Dilly, the above mentioned surcharges for inset might only be true for production cabinets, and you said you're going with true custom? In that case, any good carpenter won't spend much more time getting the inset to sit correctly than any other style, and shouldn't charge a whole lot extra. The upcharge for manufactured (production line) cabinets is for the extra human precision required in assembling and attaching an inset door.

Above information is true as far as I know, your mileage may vary, etc etc blah blah caveat. ;)

With inset, your cabinets are framed. The entire front is 3/4" board lumber with likely a board lumber door/drawer front. Occasionally, a painted door is actually medium density fiberboard.

What circuspeanut said.