Sonic CD is widely considered to be the best Sonic game of all-time. Personally, I think the honor belongs to Sonic 3 & Knuckles, but I still view Sonic CD as a magnificent entry in the Sonic series.
Sonic CD is noteworthy for a number of reasons. It was the introduction of fan favorite Metal Sonic, Sonic's sinister metallic counter part, and in my humble opinion, the most memorable of all the machine Sonics. This game also introduced Amy Rose, who would go on to be a regular in the 3D Sonic titles. There's also the time travel aspect of the game, which allows you to visit the past and future versions of each zone. Even with all that stuff the game brought to the table, Sonic CD is probably remebered most for the biggest difference between the USA and Japanese version of a game: the soundtrack. Both the American and Japanese versions of Sonic CD have different soundtracks and this has caused quiet a stir among fans over the years.
The Japanese version of Sonic CD's music was composed by Naofumi Hataya and Masafumi Ogata. The two vocal tracks, "Cosmic Eternity - Believe in Yourself" and "Sonic - You Can Do Anything" were written/performed by Keiko Utoku. The Japanese soundtrack actually sounds pretty American from my point of view. Both vocal songs are sung in English and are very catchy. The background music that plays in the zones is unlike anything you've heard in a 2D Sonic game both before and after Sonic CD's release. I actually didn't hear Sonic CD's Japanese soundtrack until almost two years ago, but I was ware of the controversery sourrounding the USA Sonic CD's music.
Sonic CD's USA score was handled by Spencer Nilsen (he also worked on the music for some of the Ecco: The Dolphin games). With the exception of all the "Past" themes, every song in the American version of Sonic CD is different from the Japanese version. GameFan, a well-loved, now defunct game magazine scored the Japanese verison of Sonic CD a 100%, but gave the USA version a score somewhere in the 70% range and it was very obvious that the score was based on the music and not the gameplay itself. A staff member of GameFan went as far as to label the USA Sonic CD tunes as "elevator music." Ouch. That's pretty harsh. Really, it's not like the American version of Sonic CD got a bum rap. We got "Sonic Boom," performed by Pastiche, for crying out loud. Sonic Boom, people! I actually find it pointless to debate between which version of Sonic CD has better music. Both soundtracks are spectacular and very few games get TWO sweet musicl scores. Rather and whine and moan about it, just enjoy both soundtracks.
What really surprises me is that there was never an official soundtrack release for either the Japanese or USA versions of Sonic CD. Even more than 15 years after Sonic CD's release, Sega has not come out with an OST for the game. Though you can easily find rips of both versions on the web.
EDIT: As of November 23, 2011, Wave Master released a 20th anniversary soundtrack for Sonic CD. It mostly contains the Japanese audio from the game with Sonic Boom as a bonus track. Also, there was a limited edition music CD called Sonic the Hedgehog Boom, which contained some extended versions of the USA's score. Finding a copy, however, will cost you.