Stability problems can be broadly broken down into four categories, reflecting the complex nature of an emulator:

This type of problem refers to a complete lock up of your PC or an operating system STOP error (BSOD), usually requiring a hard reset of the system.

There are no known bugs in Project64 (we cannot vouch for 3rd party plugins, of course) that would cause a system crash/lockup/other form of operating system failure. If you experience such a problem while using Project64, it is very likely that you have a hardware or driver or directx or operating system problem. Run diagnostic software and check that your system is stable in other Direct3D applications, games, benchmark utilities etc. Find some torture-testing utilities. Consult hardware documentation if you need further help. You could try changing plugins, and use dummy plugins to see if you can narrow down to one area thats causing the problem (doesn't mean its necessarily a fault in that area of the emulator, but that area of the complete system).

This type of problem refers to an actual crash or hang in the Project64 application, resulting in a generic Windows error messsage "this program has peformed an illegal operation" or "this program is not responding" etc. The exact type of message depends on your version of Windows, but the point is that you are seeing a Windows error message not a Project64 error message - in other words, Project64 has failed to handle an error, which could indicate a bug in Project64 or a system failure:

This type of error refers to an error in the Project64 application or plugin(s) that is handled succesfuly by the application or plugin error handlers. a good example of this is the "UnHandled OpCode" error (OK, the OpCode itself is unhandled, but the situation is handled - you can end emulation, reboot the game, or play another game, without Project64 crashing). Another example is a graphics Access Violation. This type of error neary always indicates a bug or a configuration error in the emulator.

Troubleshooting speed problems

The first thing to understand is what speed to expect from Project64 - as a rough guide, the following specifications should be just fast enough for each game at full speed with the default configuration:

Mario64 - P2-450Mhz ?
Zelda - Athlon 800Mhz ?
Perfect Dark - Athlon 1.2Ghz ?

Points:

Not all the suggestions below will improve performance for you. Some will only reduce quality, stability etc. You have to try them and see the effects for yourself.
Some of these suggestions have the potential to do damage to your hardware or software or data or all three. Any such damage that results from your following the suggestions listed on this page is entirely your own responsiblity - take care and don't do anything you are no confident you understand - seek advice from hardware internet sites etc. if you need to.
As a general rule, FPS in Project64 depends on your CPU, not your graphics card, because most users are CPU limited, not graphics card limited, but the graphics card can become the limiting factor at high resolutions with high levels of FSAA, or if you have a below minimum spec. graphics card.
The generally most significant factors are listed first, descending to the least significant (i.e. the most to the least likely to help, in my opinion and experience).

Check problem is not being caused by one of your plugins - plugins can stall the emulator by design or due to bugs in their coding.

Hardware level

increase CPU clock rate or upgrade CPU
increase font side bus/RAM clock rate
add RAM if you are short*
choose a CPU with SSE (& MMX!) capability
adjust RAM timings, cache timings etc.*
increase graphics card clock rates*
use PCI rather than ISA sound card
disable any unneeded ports/hardware
avoid IRQ sharing*
use USB rather than Gameport input devices

Driver level

update drivers, video card drivers, chipset drivers, sound drivers*
use 16 bit colour desktop rather than 24/32*
use lower level of anti-aliasing, or none at all*
disable Vsync
disable multi-display if your system supports it*
use 16 bit z buffer (rather than 24/32)*
use texture compression*
lower or raise monitor refresh rate*

Operating System level

shut down all non essential (background) processes
disable findfast/file indexing/system restore/task scheduler etc.
adjust process priorities
use Win2K/XP series OS if you have enough RAM (192MB+)
use Win98SE if you don't have enough RAM (WinME seems generally a bad choice)
update DirectX version
just rebooting Windows can help free resources
clean reinstall Windows in extreme problem cases
compact memory
fix pagefile size
move pagefile to fastest drive*
defragment hard drive
lower debug levels on DirectX
don't use debug (usually beta) builds of drivers or DirectX

Application level

don't run multiple instances of Project64
fullscreen modes may be considerably faster than windowed modes*

Emulator core

use Recompiler instead of Interpreter**
disable Limit FPS - System > Limit FPS (This will uncap the speed to that specific region)
enable Register Caching**
enable Advanced Block Linking**
enable Larger Compiler Buffer**
use less secure method to handle self-modifying code**
don't enable the expansion pack if it's not needed**
state saving and loading sometimes helps the recompiler**
disable TLB (but only if not needed!)**

plugins

use the RSP recompiler core rather than interpreter core
don't use any form of Framebuffer emulation
don't enable Audio Sync on either audio plugin
use a lower resolution
use 16 bit colour modes rather than 24/32
if you want true colour, use 32 bit rather than 24*

*effectiveness depends on system (hardware)
** effectiveness depends on game