Classic console and arcade games were designed to be displayed on older cathode ray tube (CRT) televisions, and using emulators that display on LCD or Plasma screens can alter how the games were originally intended to be viewed; upscaling from 224 pixels to HDTVs and stretching the aspect ratios to 16:9 makes pixellated game art lose a lot of it's charm. A bit of blurriness and screen curvature gives 8-bit and 16-bit images an aesthetic appeal that is lost when the game is rendered perfectly on modern displays as can be seen in this example from gaming forum NeoGAF.
Fortunately CRT filters are available for a few emulators that can recreate the bleeding colours, scanlines and other "features" of CRT displays. Blargg's NTSC Libraries offers filters that work with NES, SNES, Sega Master System, TI 99/4A, Commodore 64 and Sega Genesis emulators. MAME users can adopt MAMEUI, a MAME graphical front end that already has a CRT filter already installed. Full details on how to set this up are in the source link below.
For most casual users this level of detail is unnecessary, but for retro gamers who don't have original hardware anymore, spending an hour or so tweaking the visuals is a valuable time investment.