We did the South Fork of the American River for a full day trip. We stopped halfway for a picnic lunch -- sandwiches, potato salad, chips, cookies, etc. It's about 20 miles of Class 3, 3+ rapids. Maybe one Class 4. I never felt like I was in danger of falling out or scared. In fact I loved it!! I would have gone again the very next day and definitely plan to go again this summer
Funny you should mention that...I did the same trip with some coworkers. Unfortunately, that year (like this year!) the snowpack was significant and the waters were running fast, meaning that what were normally Class 3 ended up being an estimated Class 4+. I was quite freaked out before we went, but felt a lot better after many reassurances (even on here, this was right when I started posting) that NO ONE ever falls out.
Well, we hit a rock wrong on Troublemaker, and 4/7 folks in our boat went in. One coworker fell directly on top of me, pinned me underwater for maybe 2/3 of the first rapid, then I finally got out from under him and got the "SWIM REALLY FAST" gesture from my guide (apparently I almost hit a hole. Did not know that then, though)...swam hard to one side, got up to the rescue boat, ended up getting sucked under it, then finally they got a hold on me, but didn't have time to haul me in before we went through the second part of the rapid, so I rode that one being held onto by the rescue boat folks by my lifejacket.
I should have known better. If there is a way to almost die in a water sport context, I FIND THAT WAY (see also: Flipping Kayak in Pacific Ocean, Too Fat to Get Back On and Attempted Drowning in Wave Pool at Water Park at Age 9)
We did have lunch, though, and beer (although I was friends with the guide...he's a pro and works for one of the local guide companies, but he is also married to my coworker so he took us for free).
With that said - if I did it and survived, the less accident prone would probably be completely safe. AND up until the part where I nearly drowned, I was having a really great time. So there's that.