You used to hear about the great new sound cards all the time 15-20+ years ago, but not any more. Is there any real benefit in shelling out the extra money for a proper sound card these days, as opposed to using integrated cards? What exactly do they offer that integrated cards don't?

As an old-school PC guy, I always had an actual sound card in my machines and disabled the on-board sound because that is the way it was done. I never once questioned the logic or reasoning behind it until about 6 months ago. On whim (mostly because of incompatibility issues with Linux) I removed my Creative sound card and for the very first time in over a decade, I enabled the on-board sound card: an Analog Devices chipset with SoundMAX integrated digital audio drivers from 2004. I was absolutely shocked. Not only was the sound quality comparable to the Creative card, in many ways it was better, since the Creative drivers used up way more resources than the SoundMAX did. I have had absolutely no compatibility issues and when using my 5.1 surround sound speakers with a surround source (like a DVD or game with surround capability), the audio sounds more "real" than the sound produced by the Creative card.
Long story short, in my opinion, an actual sound card is not in th least bit necessary on a modern computer, unless you are an audio professional or someone who considers themselves an "audiophile" and you get a top of the line sound card.

Unless you are an "audiophile" who imagines he can hear the difference there's no benefit to having a dedicated sound card. 3D sound and other special effects are now handled using vendor-independent APIs such as XACT and OpenAL; you no longer need a particular brand of sound card to hear the game as intended.
Note that this only applies to DirectSound and DirectSound 3D up until XP (Vista onwards have no acceleration) or third-party APIs such as OpenAL; games using Microsoft's new XACT API have no acceleration.
Either way, the performance impact of sound processing on a Core 2 Duo-level CPU or better is laughable at best. This won't change in the future either; CPU power has increased exponentially over the years but sound demands won't go far beyond the current maximum of 192 kHz and 7.1 surround.
Compatibility is going to be based on Realtek or nothing at all; it's been years since Creative was even remotely relevant in this regard.
The proof is in the pudding: every game works on Realtek. Each and every one, from the ancient bleeping and blooping of Windows 3.x to the latest and greatest 2010 releases with 7.1 surround. Some rubbish console ports with no QA have problems with higher frequencies (resulting in some sounds being silent or garbled, or the game not even launching at all) which can be rectified by reducing the output to 48 kHz for that game; Realtek's drivers default to 48 kHz, so this problem will only be experienced by those who have deliberately raised the output frequency.

^ to those who say there is no real benefit.
FL Studio + Ableton + a hundred of plugins + thousands of effects = death to the CPU without a dedicated professional sound card. So stop bitching about that. :p

I ditched Creative because of compatibility issues (Win7) and was stuck with on board Realtek for a while because of this.
I didn't have any problems with the sound quality but some games didn't like it at all. In fact Batman AA blatantly stated as much.
I'm not saying you're not right about 99% of the titles out there, but there are always exceptions to just about any rule you could care to name. Use words like 'every' and 'always' with care.

Of course you're going to need a professional sound card for professional audio editing, but unless you are a professional sound editor, then not only do you not really need one, you actually are not going to see any significant benefit from having one.

If threads could have a summary then that should be it.

I was specifically responding to your comment on "the issue of compatibility", which implied that Realtek compatibility can be inferior to the likes of Creative (which is demonstrably untrue as you yourself noted).
While there are occasional problems with new releases this is different from GPU issues and vastly less common, and due to the nature of how sound APIs work compatibility will always be effectively 100% (with the noted exception of non-default frequencies), so saying "every game" works is not untrue. There are various examples of games that don't work on a particular GPU brand (or particular models, or particular card+OS pairs, etc.) even after a new driver is released, but there are no such examples for modern sound cards.

You don't need a dedicated sound card any more than you need dedicated graphics these days.
That said, when I built my current flagship two-and-a-half years ago. I spent quite a bit on an Auzentech X-Fi Prelude as an experiment-to find out if my ears are nearly as picky as my eyes. I couldn't tell too much of a difference over the onboard Realtek ALC889A at first, but I had crappy speakers and headphones then.
It wasn't until I got myself some Audio-Technica ATH-AD700s that the difference became obvious. Now I can't go back. EAX is okay, but what I really have to have now is CMSS-3D Headphone. Surround sound so good that I don't even want 5.1 or 7.1 speakers any more! I can only imagine how much better it would sound if I could afford something like Beyerdynamic DT880s and an amp that can drive them.
Unfortunately, it seems that older games actually leverage it better, even with ALchemy having to wrap everything from DirectSound3D to OpenAL. I get more exact audio positioning cues in the likes of Thief 1/2 and Battlefield 1942/Vietnam than I do newer games like Just Cause 2 (which sound more like rough 5/7-speaker blobs surrounding me, with no VERTICAL audio cues at all).
You heard me right-I'm saying that game audio is actually being DOWNGRADED to some extent because of the assumption that everyone uses 5.1/7.1 speakers, never mind that I prefer headphones that can give me an even more compelling surround effect with the right HRTF processing.
Now, as for performance increase...I'm not sure I notice any extra framerate in games. But you don't buy a sound card for that nowadays-you buy one because it sounds much better, like how you pay up for a better monitor or graphics card so everything looks better.
Some people are REALLY snobby about this, though, as I once found in #GOG. This goes to the point where they shun any form of internal sound card, instead opting for an external DAC. Such an approach to get away from EMI could result in better sound quality, but I won't do it unless they start putting X-Fi APUs in external sound devices since I absolutely, positively MUST have CMSS-3D Headphone. (No, Creative's own USB X-Fi products don't count-they're fakes like the XtremeAudio and burden the CPU for everything, not to mention missing many key features that true X-Fi cards have.)

Thanks for the info, everyone. It's been really helpful.