I just bought a Lynx II (my third) about 2 or 3 months ago.
I've got Pit-Fighter, Ninja Gaiden, Stun Runner (Amazing Port), Blue Lightning, and Rygar.
The Lynx will always be my favorite handheld. It was soo far ahead of it's time. The type of games that came out for this system in 1989, and thru the early 90's was mind blowing. Especially because these games had arcade quality graphics that were being done on a handheld system.
I mean Blue Lightning came out in 1989, and the graphics would have been very good if done on a console; but on a Handheld?! Stun Runner (1991) damn-near arcade perfect. Hard Drivin' (1990) Polygons on a portable?! In 1990?! Yes, it had a choppy slow frame-rate, but I got used to it. Still, seeing these type of arcade games being ported to a handheld was cool as hell to me back then.
The Ninja Gaiden beat 'em up sealed the deal for me. I loved that game in the arcade, and after reading the EGM review were it got all 8's! It was a wrap. The Lynx became a must-buy.
The 16-bit graphics chip, and the scaling and rotation was put to serious work on a few games (Stun-Runner, War-Birds, Hard Drivin', Blue Lightning, Xybots, etc.) I could go on, and on.
The Lynx will always be my favorite handheld, just because I was so blown away by what I was seeing on a handheld at the time.