Apple 2 Emulators
AppleWin https://github.com/AppleWin/AppleWin currently on version 1.24.0 and now hosted at GitHub. The newest version also emulates the Uthernet which enables an Apple 2 to connect to the Internet. AppleWin also has emulation support for Apple 2 HardDrives of up to 32megs. Of all the emulators available for Windows, AppleWin is the most advanced and simplest to use. One of the best features is the "speed-up" option which allows users to run the Apple at double, triple or as-fast-as-the-Windows-Machine-will-go speed :) No more long waits while Ultima loads!
Macintosh / MacOS Emulators
Virtual ][ is a program that emulates the vintage Apple II computer on your Mac http://www.virtualii.com/
iOS / iPad
ActiveGS - Best Of FTA To celebrate the 20 years of the *Free Tools Association*, here comes a collection of the best programs developed by the members of the FTA team : Nucleus, Modulae, Photonix, Delta Demo and much more!!! Enjoy this journey back into time ;) This is a ][gs emulator but plays all the old Apple 2 games. Couple big TRICKs to get this one to work the way you want. APP comes prepackaged with a couple //gs games, but no apparent easy way to put on old DSK files to play your favs. You'll need another program from the app store called iExplorer. The trick here is that you have to find where FTA stores the game DSK files. Jailbroken iPads with root access are great for this. Simply cd / & ls -lsatR > filelist.txt & come back in an hour and download with SCP. Anyhow... once you find the XML file & game directory you can upload new DSK files & play the old classics. The emulator comes with a "soft keyboard" & joystick which makes playing a game like Airheart great. So great that right now it's my fav emulator... since I haven't been able to play Airheart on AppleWin or cAndy Apple. Check out JerkWerks http://jerkwerks.com/finally-apple-ii-and-iigs-warez-on-your-ipad/ for a REALLY REALLY good how to.
cAndy Apple https://play.google.com/store/apps/details?id=com.zerohoh.candyapple&hl=en Relive the early Eighties with a shiny Apple //e and a stack of diskettes! Attention: Do NOT download if you are not interested in 1985-era emulation. Far and away the best emulator for the Android. Thinking that it's also the only one now. If you have a droid with a slide out keyboard the experience of playing games like Ultima is fantastic! Right now my fav game on this system is Bolo. With the keyboard I can spend a few hours hunting down tanks in a maze.
Java Apple Computer Emulator https://sites.google.com/site/brendanrobert/projects/jace Jace is a logical** reproduction of an enhanced Apple //e computer, written in Java 6 and tested on various platforms (Linux, Windows, MacOS X). Bonus with JACE is the META Cheat modules. Especially cool is the cheat mod for Prince of Persia. Developer Brandon Robert is also working on a MAME style cheating system where users can watch various memory addresses to see whats changed and then freeze them.
Epple ][ http://mosher.mine.nu/epple2/site/ Epple ][ (the Emulated Apple ][ is a free (as in GPLv3), cross-platform (Windows, Linux) emulator of the Apple ][ and Apple ][ plus computers from Apple, Inc. It strives for accurate emulation of the original machines, with a few extra features added.
No OS Required http://www.virtualapple.org/ Play old Apple 2 games online without having to download & install an emulator. Great site with a good 100 or so games including Lode Runner and a bunch of Apple ][gs games.
Apple2js http://www.scullinsteel.com/apple2/ Has a bunch of games and other disk images online. Plus it also allows users to save items locally on their computer.
Tons of Apple 2 Emulators here...