Emulators
nspire_emu
nspire_emu is currently the main TI-Nspire/CAS/Touchpad emulator. It only supports Windows. You can download it from the United-TI thread where it was born, but the thread is quite long so finding the latest version is not easy, and you need a UTI account. You may prefer to download it from the TI-Bank archives (French): choose the latest version of Emulateur Nspire/NspireCAS.
Most TI-Nspire emulators derived from nspire_emu. Note that these custom versions are not always kept up-to-date with the latest version of nspire_emu.
Ncubate
Ncubate is derived version of nspire_emu enhanced with features useful to developers, such as state saving/reloading and additional debugger commands.
Xspire
Xspire is a port of nspire_emu for the GTK+ GUI library, compatible with Windows and Linux. This port also supports skins. You can download it from the United-TI thread (account required). Note that a more recent version may be available further in the thread. The GDK/GTK+ libraries are required for it to work (Windows users should use the Windows port).
Nspire Memory Editor
The Nspire Memory Editor plugs itself into nspire_emu to offer advanced memory-related features, such as hexadecimal memory edition, string and binary search, memory chunks read and write, and string or instruction-based breakpoints. Download it from the United-TI thread (account required). Note that a more recent version may be available further in the thread.