Mini vMac is for me the best way to run Macintosh 680x0 software. Other people may have different needs and preferences. The goal of the Gryphel project, of which Mini vMac is a part, is to help preserve such software. For that goal, the more alternatives to Mini vMac the better. Here are some:
One of the most popular emulators. Originally by Christian Bauer, and later worked on by Gwenole Beauchesne, it currently has no main developer, but the community at E-Maculation continues to update it. (Basilisk II on Wikipedia)
The Multiple Emulator Super System emulates multiple computer systems and game consoles in one large program, for preserving history, emphasizing accuracy and portability. Lately there has been a lot of progress, in particular by Arbee (AKA R. Belmont), in Macintosh emulation. (MESS on E-Maculation) (MESS on Wikipedia)
The PC Emulator by Hampa Hug emulates both an IBM PC and early Macintosh models. (PCE on E-Maculation) (interview)
Upon which Mini vMac was based. The last update was in 1999.
If the above link doesn’t work for you, try this alternate vMac link.
Apple's emulator, for any PowerPC Macintosh. This can be used either on a real hardware, or an emulator such as SheepShaver or PearPC.
Keeping old computers operational can be a challenge. One resource is the 68k Macintosh Liberation Army Forums.
Shoebill is a “Macintosh II emulator that runs A/UX (and A/UX only).” A/UX is a Unix operating system from Apple (from long before OS X) that can run Macintosh software.
ARDI Executor can run some software for Macintosh 680x0 without requiring any software from Apple. (Executor on E-Maculation) (Executor on Wikipedia)
mpw is a specialized emulator for running MPW tools on OS X.
A project to emulate a Macintosh Plus in hardware, using an FPGA.