I used to run a discrete soundcard for my M-Audio BX8's but actually when I was temporarily forced to go back to an onboard Realtek codec I was impressed how good they still sounded.
By far the biggest impact to sound quality in the sub $500 range is the speakers. Only once the speakers rise above uneven response curves found (so often) in the sub-$250 range do the differences between a cheap soundcard* and a quality one matter.
Yup, always amuses me when people talk about buying expensive soundcards with fancy DACs and user-replaceable op-amps, when it isn't going to make a damn bit of difference due to the cheap speakers/headphones they're using.
That said, some aggressive EQing can often make even sub-$100 speakers sound halfway reasonable.
* - the issue with onboard sound is not usually the sound quality but the interference that the analogue outputs pick up from the motherboard. Some solutions are shielded better than others, unfortunately.
Yes, fortunately the quality of onboard audio has improved tremendously over the years. Older (from ~10 years ago) mobos tended to have a laundry list of issues -- poor bass response, harsh high end, distortion from crappy DACs, tons of analog interference -- but those days are behind us now.
You do still find the occasional mobo that has analog interference issues, but even when it is present it is typically low enough that it is only audible through headphones with the gain cranked way up. Most analog interference problems on contemporary hardware turn out to be due to badly shielded front panel audio jacks/cables (i.e. a problem with the case, not the mobo), and can be solved by plugging into the rear panel jacks instead.
These days I tend to just stick with onboard unless I'm setting up a system where I will be recording from the line in jack (in which case I install my old Turtle Beach Santa Cruz or M-Audio Revolution).