I've had minor issues with the Dolphin emulator, got stuck sound looping in Super Mario Sunshine; and an earlier version didn't handle 1080 Avalanche very well, but aside from that it's been all right.
For N64 games I've only ever tried Project64 WARNING, DO NOT DOWNLOAD, READ REST OF COMMENT TO LEARN WHY, and while it's done an all right job, it has by no means been flawless. Best example is DK64, which I've recently learned was a poorly coded game in the first place, has numerous bugs (I experienced being sent back to the start of the level for climbing a tree, it probably voided me out somehow). Also it seems that the devs have sold out, and are now including an installer that also installs other stuff, including rootkit malware that is exceptionally difficult to remove. (It's possible to avoid it by opting out and declining the install, but the installer is being deliberately vague about what exactly is happening). (Thread about it here [http://forum.pj64-emu.com/showthread.php?t=4390]. If this link is in violation of forum guidelines, please notify me and I will remove it).
I've heard about other options, but I don't remember their names.