I've made a Spotify playlist with a 6 hour introduction to the entire history of classical music*. If the classical repertoire is anything for you at all, you'll find something here. [Here's a pretty good WIMP subset of the list, and here's an Rdio version]

The standout classical record label is Deutsche Grammophon - Just DG among friends - and they have recently done a great service to classical music, by putting out a collection of 55 CDs in celebration of 111 years of operation.
It's quite a remarkable collection. From DGs amazing catalog of recordings you get the top performers of stand out works, from pretty much all of musical history, "classical" musical history that is - but that stretches from medieval times to West Side Story, so a solid 500 years worth of music. There's a lot of gold there. Great performers. Great music.

I'm always trying to convince people that they're really missing out, by not checking out the classical repertoire, and this box set is a convenient way for you to find what type of classical music is for you. If you don't find it here, I'd say you're unlikely to find it - except the modern dissonant stuff, which is curiously absent. No Schönberg, Berg, Webern, Stockhausen. No Bartok even, or Shostakovich. No Ligeti. None of the American serial music. But with those caveats, this box set really is it. The mainstream is solidly represented. If this leaves you cold, that makes me a little sad, but I will just have to accept that classical really is not for you.

However, 55 CDs is still a lot of sound to chew your way through. With that problem in mind, I've condensed the CD set - neatly packaged in themed discs of similar music - into just 53 tracks. 6 hours of music. I did this by choosing exactly one cut from each CD, leaving out only two CDs that were the second disc of 2-disc works. I'm still happy to make the same claim about the 6 hours I do about the 55 discs. If these 6 hours leave you cold, you're never going to have much fun in the concert hall.
If, on the other hand, you find something you like, you're going to find a lot more. I am going to try to make suggestions for further listening for all of the 53 tracks in the next couple of days. If you already listen to classical music, feel free to make suggestions in the comments below. If you have questions about the music, or my choice of tracks, feel free to ask.

Final note, if you're not on Spotify, where you can listen to all 55 CDs: The box set is cheap - 600-700 DKK for all 55 CDs in Danish stores - and also conveniently available as MP3s from DGs online store. DG has been at the forefront of just accepting the future, and have been issuing high quality DRM-free MP3s (or FLAC lossless) in their online store for years. (Stupid interaction alert: 1. Choose country before trying to buy. 2. You can only buy from the search page, not the album info pages).

Final bonus playlist: These are my 2 hours worth of personal favourites from the 6 hour selection.

* Well, as the post explains, the dissonant 20th century and present got left out. I'll have to make a separate playlist for that.