Has there ever been a 2D shooter you've always wanted to play with someone? Maybe you've had trouble finding anyone to play it with, let alone someone skilled. Use this thread to arrange games with others!
There is a huge world of playing shooters online through emulation. Here's what you need for various game platforms:
Arcade Shooters
MAMEHub – A new netplay solution for both MAME and MESS, this emulator has excellent netcode and rarely desyncs. When desyncs do happen, it fixes them in real time so your game isn't ruined. This emulator is continually being worked on and stays updated with the latest MAME builds. While MAMEHub is still in beta, it already works exceptionally. While a lot of emulators are Windows-only, MAMEHub even has Mac and Linux ports, and you can play cross-platform! It requires a bit of work to setup, including port forwarding, but I would recommend it for just about anything arcade except for a select few games that netplay is currently broken for.
MAME32k – An ancient Kaillera-based build of MAME, it rarely desyncs, but it has poor game support due to being based on a very old version of MAME (0.67). Most people, including myself, use 0.64 instead of 0.67. I'm not sure entirely why/can't remember. I used MAME32k a lot in the past, but I have not found any reason to use it again since MAMEHub came out.
MAME++ – Another Kaillera-based build of MAME, this emulator likes to desync, but it has much better game support. This is based on MAME 0.119.
SNES Shooters
ZSNES 1.36 or 1.42 – While ZSNES hasn’t been updated in a while, it’s the best emulator by far for SNES netplay. Versions 1.42 and 1.36 are the ones you want for netplay. 1.42 likes to desync on some games, but 1.36’s netcode is rock-solid. Are there actually any SNES shooters that allow co-op? You could play Strike Gunner S.T.G., Raiden Trad, and umm... Darius Twin

NES Shooters
NEStopia – Another Kaillera-based emulator, this has very basic netplay functionality, and it can desync. You may actually be better off using MAMEHub for NES netplay at this point.
FCE Ultra – This has netplay? Supposedly it does, but I’ve never gotten it to work right. Note that netplay is broken in FCE UltraX.
Playstation Shooters
ePSXe – This is the go-to emulator for Playstation netplay, but I have had trouble with desyncs when using it in the past. Uses Kaillera for netplay. Experiment at your own discretion.
Playstation 2 Shooters
PCSX2 - I have no hands-on experience with Playstation 2 emulation at the moment due to not having a powerful enough computer, but I know PCSX2 has a plugin that allows for netplay.
Dreamcast/NAOMI Shooters
NullDC - I don't have much personal experience with this, but I hear it has few desyncs. Lacks a GUI, so you have to edit a text file with the other player's IP at the moment.
Demul - Requires a more powerful computer than NullDC, and I have heard that it has more trouble with desyncs, but I have not actually tested it myself. There is a setup guide here.
This topic post will be subject to future editing. If you have experience with other emulators for 2D shooter netplay, please post about them and I’ll add them. I'll probably put system/connection speed requirements for each emulator eventually if someone can get me that kind of information.