What well-known ICs have essentially no packaging?

You can actually buy unpackaged ICs. They are sold as "bare die". Basically this means that the silicon has not been wire bonded into a package nor covered up.

I've come across a few things including a few TI ICs that are available as bare dies. In fact there is a whole page on the TI Website which lists parts they sell in this format. Other manufactures (e.g. NXP, Microchip, etc.) will also likely sell bare die versions of some of their ICs.

However, I'm not entirely sure whether any of these will be available in small quantities. Typically bare die stuff will only be used in very niche markets by people with the equipment to wire bond them. It is likely that you would have to need 1k+ units before the companies would be willing to sell them to you. In fact the reason most ICs are available in small quantities (other than samples) is that the big distributors buy in bulk and then resell to low volume customers.

A more economical option if you are just interested in looking at them (which is not surprising, they can be quite spectacular!), is to look on a well know auction site for "Silicon Wafer". There are quite a large number of processed (but electrically defunct) 6", 8" and larger wafers for reasonable prices (sub $30). These are even more spectacular than just a single die.

UVPROMs (Ultra-violet erasable read-only memorys) had a quartz window through which you could see the actual silicon chip.

A lot of the old (70's and 80's) uP, RAM and such were produced in ceramic packages for hi-rel or hi-temp use. These ceramic packages are easy to distinguish, since the ceramic is usually white or grey, not black. The chip is installed in a well in the middle of the package, and a piece of metal foil soldered around the edges covers it. If you clamp the IC down, it is usually possible to peel the foil away using an exacto knife or something similar.

In general, you're best off looking at old chips. The newest (as in the last decade or better) are made with such fine features, like 14 nm nowadays, that details are simply invisible in visible light.

eBay is probably a good place to start looking.