Is it possible to play Apple IIe disks on a new Mac?

No

Mutant_Pie

P.S. You can however use a Compact Flash card to transfer files between an Apple //e and a Mac (I think that only OS 9 can read the Pro-DOS formatted CF cards, so you can only do this on a dual boot (not modern) Mac). Look through this forum for discussions on the Apple II Compact Flash Card interface.

P.P.S. There are several emulators for the Apple II that run on Macs.

Yes, it is possible. There are many ways to do this. CFFA is a good option, here is what I did...

I have a serial card on the Apple II. I bought a serial to USB adaptor to connect to my Mac. I wrote some custom software to copy my DOS 3.3 disks over to the Mac as .dsk files which can be used with the plethora of Apple II emulators.

Game disks with copy protection are more challenging to bring across. Either, make a nibble copy and save the disk as a .nib file. Some of the emulators will use the .nib format and may emulate the half and quarter tracking and other nastiness that those old copy protection schemes would do. Or, acquire a "cracked" version of the game where the authors no longer mind you making copies.

You might be able to get away with not paying anything. If you can find the games you're looking for (ftp://ftp.apple.asimov.net/pub/apple_II) you're good to go with an emulator. If you have your own disks you want to use, you can do as mmphosis did and write your own transfer software. If you're less adventuresome, you can pick up a super serial card and a serial adapter for the Mac (i.e. Lindy, Keyspan) and use ADTPro (http://adtpro.sourceforge.net) to transfer the disks yourself.

... you could always just buy a used Apple IIe (IIc, IIGS, etc) on eBay. Probably be the less problematic and you would get all the thrill of retro computing.

As I said in my original submission, I have an Apple IIe that is in perfect working order. I just want an updated computer but have the ability to play these disks.