So how well do the games work? Here are the ones you should definitely try:
This looks pretty good, aided no doubt by the smaller game window currently necessary for Remote Play. Fighting actually feels reasonably responsive due to the long attack animations, so you can perform your favourite moves without too much trouble. Don't expect to be able to parry deliberately, however - there's zero chance of your reaction time and the lag making for a pin-point counter. Try Tekken 2 too - it's even more command-string based.
Metal Gear Solid
Snake's first 3D outing looks really impressive on the small screen and the slower-paced gameplay makes the lag workable. Only just, mind you - you'll often overstep the shelter of a corner and into plain sight because you forgot to let go early enough. You'll also need to select Type 2 from the control options, or you won't be able to access your inventory with the triggers. Still, it is playable and this taste of handheld MGS1 has got us excited about seeing the full game on PSN.
Above: Ugly artifacting like this occurs over remote play, especially on lower quality settings. If you stay still, it gets sharper, though