Not most, but many campgrounds now offer wireless internet access. There is a file in our library that lists 700 campgrounds with free wireless internet and this web site has several files for Street Atlas and Streets & Trips that show campgrounds with both free and pay wireless internet.
If you'd like to explore the satellite internet option that John mentioned, click here for contact information for a HughesNet certified installer. A number of us here have had very positive experience with his work and support.
Also check out Wireless Air Cards. Personally I use Sprint (a USB connected antenna and electronics (including GPS) that I can hang in a window in the rig, use out on the picnic table, or use in the truck when traveling. Cost me $50 bucks up front and $60 a month for air time, vice $5,300 or so up front and $80 a month for the automatic DataStorm satellite internet system, or $1,300 up front and $60 a month for the Tripod satellite internet system.
Can I use my Air Card EVERYWHERE like satellite internet? NO, I can't! I have to be someplace that has sprint coverage, but given my travel habits I'm finding I usually have coverage. If I don't, which as been rare, it's always been a short drive away. To be honest I've had a harder time finding Wi-fi, at least Wi-Fi I can use from inside the rig, than I have coverage for the Air Card!
Another and possibly better choice, given the size of their network, is Verizon. The Air Card I have is EV-DO, and it's very very fast. MUCH faster than I thought it was going to be. I'm not sure what protocols Verizon uses, but I doubt it makes a difference.