Mupen64Plus is a cross-platform, open source emulator based on Hacktarux's Mupen64.Version 2.3 has various fixes over version 1.6.1 and is overall more accurate, even outclassing Mupen64Plus in some instances. It works well in WINE for the most part, but if you're on a different platform, use Mupen64Plus instead. However, it presently remains confined to Windows, though work is underway to port it to Android and Linux. It is currently very actively developed, is capable of using a wide variety of plugins, and has a relatively user-friendly interface.
Although many Nintendo 64 emulators have been made and many games can be run between them, complete compatibility and/or accuracy still leaves a bit to be desired.