Pumpkins and watermelon of very good examples of 2 garden annuals that can grow a very impressive root system. However, altho' I have pumpkins most every year, I don't have much experience with watermelon. Especially, if your question has to do with tilling around the plants for weed control. Still, I would think that you can get down in the ground quite a bit without worrying much about damaging too many roots.
If you are thinking about water needs, take a moment to find the recent topic on cucumbers, etc. on the forum. But, here are some direct answers on your question from North Carolina State University (link):
Both crops have a "Rooting Depth" of "D = deep, 24 inches plus."
The horticulturalists measure rooting depth as both a maximum and an effective. Effective depth is what the plants are usually down to and it typically seems to be about 1/2 of the maximum. Unless you are giving the plants constant shallow irrigation, they can go looking for moisture to a really good depth. I have seen pumpkin fields around here where irrigation was only turned on a couple of times thru the season. A good soaking and then weeks with no water - the plants must send there roots very deep.
Naughty, as my teachers used to say, there is no such thing as a stupid question. Steve, you always seem to have some great source of information for all of us. Thanks.
What I'd like to do is convince people that all necessary information is to be found right here in the Pacific NorthWest. Couldn't be further from the truth .
There's this really super "table #2" that Washington State University has on Soil Water Monitoring and Measurement (link). Unfortunately, WSU leaves pumpkins and watermelons completely off their table!!
The roots on AG's (Atlantic Giants) are huge. They will grow as deep as the soil will allow. I have a hard pan at about 10-12" and the roots hit that then turn. I have found roots as long as 10 feet. I once did a study on the roots of AG's to try to improve feeding and watering effectiveness. I'll see if I can find it and post some of the pictures and information I discovered.