I don't mind the newer onboard sound, to be honest. For general use it is really quite nice for something that comes included.
However, if you're in need of higher quality sound, there are a few affordable options out there. I don't know of any cards designed specifically for headset use, but I have used a couple cards that I know worked well with both speakers and headsets.
Newegg.com - Creative Sound Blaster X-Fi XtremeGamer 7.1 Channels 24-bit 96KHz PCI Interface Sound Card - Sound Cards
This card is basically a stripped down X-Fi Titanium, but rest assured it has the same chipset. It replaced the Xtreme Music cards in the lineup since so many people used them to game they just renamed it. I used this card for a couple years until I got my current card for home studio recording.
A quote from the advertisement, "The card's audio processor, with help from Creative's CMSS-3D technology, is able to remix your stereo audio into surround sound—even through stereo headphones. This is ideal for playing first-person shooters so you can hear your enemies before it's too late. EAX Advanced HD technology further improves game audio tracks providing a more immersive experience."
I thought headsets sounded pretty great on this card, even when I was using cheapo 20 dollar sets.
Avoid "X-Fi Xtreme Audio" cards, as they don't have the same chipset as the higher end X-Fi's.
Years ago I used a Turtle Beach Santa Cruz card and liked it quite a bit, but I can't comment on their current line-up.
My current card, if you're looking for home studio recording, is an M-Audio.
Newegg.com - M-AUDIO Delta 1010LT 24-bit 96KHz PCI Interface 10-In-10-Out PCI Virtual Studio - Sound Cards
It really sounds great, both in and out. Games and music sound wonderful through my Altec Lansing 4.1 speakers that are 9 years old, and through my headphones (currently using relatively cheap 40 dollar pair for games). You might have problems with the input and output options, but if this is a route you'd like you take you can check out their full lineup for various options.