Like a lot of people here in the US, I missed out on the Sega Saturn when it was still in production. As a kid, I always wondered what games I was missing out on, since we had a PlayStation. I was a huge fan of the Sonic the Hedgehog games on Sega Genesis, and seeing how the Saturn was also a Sega console, I thought I was missing out on some cool Sonic games. Turns out that, well, I really wasn't. The only game I really missed out for years was Sonic Jam, which was just a compilation of the original Genesis Sonic the Hedgehog titles, with a small 3D level to explore thrown in. (Interestingly, I've heard that this 3D level was the result of a game Sonic Team was working on, that eventually became Sonic Adventure on the Dreamcast.) The only other two Sonic games for Saturn I played on PC; Sonic 3D Blast and, of course, Sonic R.
Indeed, my first experience with Sonic R was on the PC, which is probably the worst way to experience it. To put it simply, Sonic and friends control like cars. Much like the F-Zero series, you use the shoulder buttons to 'lean' left and right, for more turning power. First of all, this makes no sense for a game where you're controlling a character directly, and secondly using this control method with a keyboard isn't exactly self explanatory. I don't recall the default PC controls, but thankfully you can remap them to something more comfortable. Anyway, PC version aside, the controls feel very stiff. Controlling the characters feels very heavy, like you have to fight with them to make them move where you want. The shoulder button leaning offers some concession, but you'll still have a hard time not running into walls.
As seems the tradition for Saturn games, Sonic R is very short on content. There are only five tracks to race on, including the one unlockable track. However, the levels offer some replayability to them. Each level, except the last one, contains five coins (featuring Sonic's face), and at least one chaos emerald. Two of the tracks feature two emeralds. These collectables are where the real enjoyment of the game comes in; unlocking all of the bonus content. Finishing first in the first four tracks unlocks the fifth. Collecting the five tokens in a race and placing at least third will lead you to a challenge race with one of the hidden characters. Win the race, and you unlock that character. And finally, collecting all the chaos emeralds (which also requires placing in the same race you collect each one, frustratingly) will unlock Super Sonic. Assuming you can master the stiff controls, all of this will only take a few hours to complete. There is also a two player split-screen mode, and it's exactly how it sounds -- You and a friend race eachother.
Unlocking characters actually matters, since each character has different stats and their own special ability. If you're familiar with the characters, the abilities aren't super surprising. Sonic's the fastest, of course, and has a double jump, Knuckles can glide, Tails can fly. Other tertiary characters make an appearance, like Amy Rose who drives in a car that can float above water. Dr. Robotnik is a playable character, and can fire missiles at the other racers, which sounds unbalanced but is actually not very effective. The unlockable racers are basically robot versions of the main characters: Metal Sonic, Metal Knuckles, Tails Doll, and Egg Robo. They feature mostly the same abilities, but can usually float above water, and are usually better. I must make special mention of Tails Doll, who's a creepy lifeless doll who floats around like a ghost. Super Sonic, however, is broken; he's Sonic, double jump and all, but even faster. The opponent AI can vary from absolutely asinine, to almost cheating. Sometimes your opponents will literally go in circles, other times they'll take genius shortcuts that you never would have thought of, especially in the one versus one races to unlock characters.
All in all, Sonic R is very short on content. I would only recommend the Sega Saturn version to serious Sonic collectors. However, you can pick it up as part of Sonic Gems Collection for Gamecube (and PS2 if you're in Europe), which can be a great deal since it also comes with the fantastic Sonic CD (admittedly not the 'definitive edition') and the 3D arcade fighter Sonic the Fighters, as well as several of the Game Gear titles.
Screenshots from GameFAQs.com.