Tony Hawk's Pro Skater (PS1, 1999)
So it's difficult to overstate just how profound an impact Tony Hawk's Pro Skater had - not just on skateboarding games, but on any sort of "extreme" sports (just take a look at the name-sponsored BMX, snowboarding, etc. games that followed in its wake). It's simple: the game practically created a new genre. Which should be enough to go on, but it also happens to be a masterpiece in its own right, and one of the greatest action games ever made.
After getting a feel for the near-perfect physics engine - where your landing is just as important as pulling off tricks - you'll start to take a look at those objectives ("tapes") and understand how best to get any number of them within the allotted two minutes. Each level offers the same five: two score-based tapes, collecting S-K-A-T-E letters around the level, finding a hidden tape, and activating five switches specific to each level (grinding 5 tables, destroying 5 boxes, etc.). The first level puts one of the boxes on a level just beyond a half-pipe - a perfect way of teaching the player how to do a transfer without any BS hand-holding tutorial; the hidden tape also makes for a perfect demonstration of how momentum works in the game.
Until its release in 1999, there hadn't really been anything like THPS's gameplay. It's the kind of action that seems suitable for arcade - addictive, easy to pick up and difficult to master, and infinitely flexible. Yet it has the type of polished physics and thoughtful level design that would be out of place in some quarter-munching machine. In short, it strikes a perfect balance between sim and arcade. Neversoft didn't really strive for realism (maybe Thrasher, released for the PS1 in 2000, is more your cup of tea... if the idea of your board breaking from one too many bails sounds like fun), but rather authenticity - the pro names, brand sponsors, and punk soundtrack help in that regard. But it's also one of the best animated games on the system, and though no one in real life is regularly pulling off 720 double-kickflips+B/S methods, there aren't any ridiculous triple backflips or uphill grinds here. The music isn't really my thing, but the audio design (overlooked most of the time) is spot-on and damn-near reality-accurate.
But all that's not really important for those who of us who have very little interest in skateboarding itself; it still functions as an action game first and foremost, and one of the finest around.
The game, like pretty much everything else, was "ported" to the Game Boy Color. It plays as well as you'd expect: which is to say it's a miserable piece of shit that should never have been sold to consumers. It consists of two modes - a simple half-pipe trial that redefines the word "basic," and an atrocious overhead racing mode; the simple act of successfully jumping off a ramp is rewarded with a static image of Tony Hawk mid-trick. No really that's the entire game. Don't bother.
All screenshots are my own. Box art from GameFAQs. Screenshots are from the PS1 version. It runs nearly flawlessly, though the Dreamcast and X-Box ports are, naturally, beefier. I didn't test the N64 version; I'm not sure why anyone would even want to.