Even if the emulation is good (which, being a multi-system emulator, isn't likely)
I haven't really used it for most of the systems it emulates, but I can vouch for its PS1 emulation at least. It's easily best-in-class for accurate PS1 emulation. It's the only one I've tried that can run both Shockwave Assault and [i]Ore no Ryouri[/i] correctly.
Mednafen is an odd beast, as multi-system emulators go. Its focus has never been on having the most features like many emulators, or on emulating systems just to say it does. It aims for quality, accurate emulation of the systems it supports, and at least where PS1 is concerned, it definitely achieves it. It's a bit of a pain to configure, but ultimately I think it's worth the effort considering the alternatives for PS1.
There are a couple of frontends out there for it; that's probably the best way to use it, unless you wanna deal with manually editing config files.