As you read through this post, by the way, please keep in mind that the games mentioned here represent a selection of my personal favorites for the system in question. In other words, I don't necessarily think they are among the PC Engine's "best," although that may be the case when it comes to one or two of them.
1. Coryoon--The good news about this Naxat-made shmup: it's one of the cutest and most colorful examples of the genre. The bad news: it'll cost you a pretty penny if you want to get your hands on a copy. As such, it's hard to recommend unless you've got deep pockets and also consider yourself a huge fan of horizontal cute 'em ups in the vein of Parodius or, especially, PC Denjin (aka Air Zonk).
2. Gekisha Boy--It's no secret that the PC Engine was home to a lot of weird games. Unfortunately, a good number of them aren't worth more than a few minutes (if that) of your time. This "action photography" title, developed by Tomcat System and published by Irem, is quite the opposite thanks to its ably drawn graphics and its unique-even-today gameplay (that tasks players with snapping photos of interesting people and events while avoiding various obstacles).
3. Hany on the Road--Speaking of weird PC Engine games, this particular HuCard belongs in the "Weird PC Engine Game" Hall of Fame should one ever be created. That's due in part to the game's protagonist, a toddling haniwa figure that looks more than a bit like an anthropomorphic condom, but it's also due to its gameplay, which appealingly recalls (while also approving upon) the platforming antics of classic quarter-munchers like Capcom's SonSon and Konami's Mr. Goemon. (For more on this game, by the way, read my "Great Gaymathon" review of it here.)
4. Saigo no Nindou--Better known as Ninja Spirit in the west, this beautiful hack-and-slash side-scroller seemingly owes more than a smidge of gratitude to the Ninja Gaiden and Shinobi series. (That said, all three games were released around the same time, with Shinobi coming first in 1987 and the other two following in 1988.) Calling Ninja Spirit a mere rip-off does it a tremendous disservice, though, as it's an enjoyable, high-quality title despite its thematic similarities to the aforementioned games. Two stand-out aspects of this Irem-developed title: its darkly detailed graphics and its somber soundtrack.
5. Son Son II--I have to say, it took me some time to gain an appreciation for this Capcom/NEC Avenue platformer. My original problem with it, strangely enough, was its HUD, which takes up a little less than a fifth of the screen. If memory serves, I also found myself a bit stumped by the first level (as in, I couldn't find my way out of it). Once I discovered the key to entering doors (you have to press and hold "up" on the d-pad for a few seconds), though, I was on my way--both literally and figuratively. Anyway, the highlights of this HuCard, in my opinion, are its huge, branching stages and its abundance of secrets, although I also like its bright graphics and suitably epic background tunes.
Honorable mentions: Alien Crush, Double Dungeons, Final Match Tennis and Mr. Heli no Daibouken