1. Light guns
Even on consoles as late as the Sega Saturn, the light guns were design around the timings of CRT refresh rates and thus many (albeit not all) LCD screen are not compatible. I would imagine this could be a real issue for collectors / restorers of cabinets as shooting games (eg Virtua Cop) were quite popular in arcades.
2. Early 3D systems as used on Sega Scope for the Sega Master System; and the Nintendo 3D System for the Famicom (Japanese NES)
These devices are less common and as far as I'm aware only available on home consoles. For those of you who don't know what I'm talking about, it's active shutter glasses (ie disabled one eye at a time) and was timed around the interlacing on CRTs. At 50/60Hz (depending on your region) the effect can be a little unpleasant. But it's also pretty amazing to play when you consider the devices are approximately 30 years old.