I got the iPad 1 a month or two after it came out and immediately put a screen protector on it. Ditto for all of my smartphones.
About a year ago, I bought a Windows 8.1 tablet and didn't put a screen protector on it. So far, no scratches. The way that Gorilla Glass keeps improving, as well as what sapphire appears to provide, I doubt that I'll ever go back to putting screen protectors on my tablets or phones. My current phone is a Nexus 4, which a lot of owners say has a screen and back that are easily cracked. But I dropped mine screen first onto a ceramic tile floor, and fortunately nothing happened.
The iPad 1 is built like a tank. My wife bought me a case, but I don't use it very often. Just one small scratch. I haven't handled any other iPads, so I don't know how they hold up.
The Windows tablet is a Lenovo Lynx and has a plastic body. It initially felt flimsy and seemed prone to damage, as many reviewers speculated. But a year later, the back has no scratches or cracks. I've never bought a case for it.
YMMV, of course. The main factor is how and where you'll be using it. For example, if I used a tablet on a train commute five days a week, I definitely would have it in a case at all times. Ditto if I were planning to sell it every time a model came out.
I also talk with a lot of school districts that provide students with iPads. Although they all say that breakage is in the low single-digit percentages, they also say that cases are a major reason why.