Well, for me it started with the GT. A lot of games magazines would cover PC Engine games as GT games, especially if they had a handhelds supplement.
So the first I'd ever heard of it was that it was the best handheld on the market (and in terms of "mainstream" handhelds, it held on to this title for years).
Then one day, I was in a well-known second-hand chain store when I saw a boxed PC Engine GT with 7 games (afterburner, PC Kid 2, Shinobi, Son Son II, Bari bari denetsu, and Cyber Core) for £70. It was my Birthday in a month, and I dropped to my knees, begging my dad for it, and he asked me if I was sure, I was, etc etc, and those 5 minutes while he went to the cash point were the longest in my life. I stood by the glass case it was in, ready to wrestle it from anyone who would take it from me.
Then we got it home, and mind == blown. Easily the best handheld. It didn't get played too much because of the battery situation (and the fact that it said not to use rechargables and I didn't want to break it. The PSU is also non-standard, so I never got one that worked right.
Then a few years later, I got a boxed core grafx (£40), and blew the PSU when I tried to plug the AC adaptor into a "shaving converter" (2 pin DC to 3 pin AC) without a stepdown. Fearing I'd blown it and with no way to play it, it went on the shelf.
Well, all these years later, I found that I can use a Mega Drive adaptor, got me a few more games, and got the Core Grafx back from my parents house, and I've got the bug again. Now I have a disposable income, I'm buying all the stuff I wanted when I was younger and on £10,000 a year (except the stuff which is £ridiculous, like a wondermega). Living the dream.
Also, aside from that, I believe it has the best versions of many games that I want to play, including New Zealand story Rainbow Islands, Pomping World, etc etc. Also, I was big into Amigas, and it seems that there is quite a correlation between the two systems - like the Amiga is the UK PC Engine in a strange way. A lot of amiga versions seem to be from PCE.