I've inherited old Corningware from the 1960s. What can or can't I do with it? Microwave? Bake? Freeze? Electric or gas stovetop? Other? ?

You've got the "Coneflower" Corningware design.

Vintage and Collectible.

Bake, Broil, Store, Serve and Freeze only.

My mom had the whole set and I've never seen her use them on the stove top.

You probably have a small fortune if you sold those to the right collector.

This stuff is amazing and I have a whole collection of a different pattern that I've accumulated over the years mostly from Ebay.

I typically don't use mine on the stovetop, although I've got a couple of two to four cup "pots" with handles that are clearly made to do just that.

I use in the oven, microwave and freezer with no problem.  What I love about them is they can go from freezer to microwave.  I most often use my smaller ones, like a single serving, for leftovers that I can take to work for lunch of save for future dinners. 

If I were bent on using this stuff on the stovetop I'd go a couple google reads first.

Short of cracking it, Corningware is good forever. I have baking dishes my Mom got for her wedding-in 1957, still good. 

That being said however, you Cannot put them on a stovetop. 

I Have 2 who are exactly the same as yours 

 Oven 

 microwave 

freezing food 

BUT do not ever put those Corning ware on the top stove 

I suggest you consult their website. Thank you for the image; it brings back memories. 

probably the same things you can do with them now

Microwave? Bake? Freeze? -- acceptable.

Electric or gas stovetop? -- Hell No.