For me, it's both wired and wireless. I don't think it's directly to do with wifi, may be more to do with what hardware you've got on your machine. See below.
I was using wireless (Time Capsule, 1st gen) and getting this problem. But directly plugging ethernet into my router (bypassing the time capsule altogether) also failed to resolve. I have a macbook pro (unibody) from 2008 (10.6.8/latest updates), no other known issues. And the same router works fine for my 2007 (white body intel core2duo) imac (10.6.8/latest updates) right next to the laptop - I can sleep/wakeup the imac as much as I like, internet (specifically, DNS) returns within seconds. I was hoping Lion might fix this for my MBP, but it doesn't sound like that's a surefire solution and don't want to spring for the $$ if it'll still be broken.
This issue appeared for me sometime after Jan 9, 2012. I had no problems waking from sleep before this date.
The issue typicaly appears after a long sleep, but sometimes even a short sleep is a problem. Restarting is the only option that always works.
It's definitely a DNS issue for me, since I can still ping 8.8.8.8, The posted workarounds (e.g., various "mDNSresponder" calls from Terminal) have usually not worked, though a few times I think the "sudo launchctl load /System.../com.apple.mDNSResponder.plist" followed by an unload did seem to work. But not in the past few weeks.
Hope this helps someone else figure out what's going on. I've tried everything else I've found in the forums - recreating my network, passwords, fixing permissions, trashing the time capsule plist, etc. This issue has been around so long (years from the dates of some posts), I wonder why apple hasn't fixed it by now.