There are some old parts from the 74 family which were never brought over (like the 7447 seven-segment decoder), but all of the basic logic parts are still around.
4-Bit Arithmetic Logic Unit http://ee-classes.usc.edu/ee459/library/datasheets/DM74LS181...
Unfortunately, it's one of the parts that never made it past the 74LS family. :(
With that said, the capstone project for my college electronics course was to build a 4-bit computer from 74LS chips, and we used the '181. The instructor explained that it was a necessary simplification, in order to get the project into the space and time available. We were provided with the schematic, but were expected to get it working with little or no help, and to demonstrate operation of a program. I wrote a dice game.
If you jumped to the 74381 you could get nifty things like the IDT7381 or L4C381, which are the equivalent of 4 '381s in a PLCC package that ran at a 25ns cycle (faster, I think, as well).
Hardware freedom will become increasingly important in the future, and I predict it will be harder to achieve that software freedom.
I remember working out the logic of "JK" flip-flops and the like. At one time I'd acquired some ancient vacuum tube versions of said flip-flops. Wish I'd kept them, they'd be a great curiosity today, a collector's item of sorts.
Should evoke some good memories looking through the catalogs of current versions of those venerable products. Won't be surprising if they'll be around for a long time into the future.
This is the technology in the common 74' series integrated circuits that became popular in the late 1960's and 1970's. You can get basic IC's that perform AND, NOT, XOR operations but also more complex IC's that perform as multiplexors, buffers, registers and so forth. You can find these in computers like the PDP or VAX series machines.
They are not used as much today and so less of them are still manufactured.
(fwiw it sounds like you know what you're talking about; I just wanted to share this info for anyone else who might be interested)
Today you can get the basic logic, of course, because a little bit of glue and duct tape is still necessary. And the super basic shift registers and I/O buffers are still useful. But all computation has moved into much more highly integrated chips or FPGAs.