On my past 3 Android phones, I haven't ever used Screen Protectors. I hate the feel and look of most of them (I know there are certain that are glass, or feel pretty much fine, but many never feel like awesome smooth glass, almost a texture sometimes), and I sometimes feel cases end up pushing up the edges, making it look like **** and needing to be replaced. Or it gets tweaked sliding it in and out of my pocket.
For good measure, WM HTC Touch Pro ended up with zero scratches on screen, lived in a case at first, then without because it was such a brick. It had a SP at first, but eventually it peeled and I said **** it. Phone felt better without (Resistive Screen with stylus). It died when I gave it to my GF for a loaner, and she dropped it and left it in a river for awhile...on the first day she had it. (my phones are in constant peril!)
The HTC Aria ended up with zero scratches and still in mint cond when I moved on to an HTC Inspire 4G. Had been dropped onto Concrete, wood, etc from at least 4 feet on occasion. Protected by HTC TPU smoked case from ATT store for entire life.
HTC Inspire 4G ended up with one very slight vertical scratch toward the far right side of the screen. I only noticed it when the screen was off, never noticed it with my finger sliding onto it, or in general use. It had a rough life, and I was happy/surprised that was the only damage it ever received. Standard drops from about 4 feet onto assorted surfaces like concrete, hardwood floors, etc. Protected by Case-Mate Tough Case from ATT store for entire life.
My GNote is still without a scratch. Has only really been dropped on carpet, and a few small drops onto hardwood floors from about 3 feet. Protected by Speck Candyshell from ATT store, then Trident Aegis (kinda **** imo), and now Cruzerlite Androidified TPU (sucked at first, broken in and a few mods with the punch from a hole puncher, now perfect).
I keep all of my phones in my front right jeans pocket with the screen against my leg, and I never leave the ATT store without a case (even if I know I'll be getting a diff case very soon). I never put anything else in my phone pocket. Also be aware if your pants have very sharp/exposed rivets above your pocket. Clean out your pockets before you wear them. Turn them inside out if you can/use packing tape or something to make sure all the possible grit/**** is gone. It's entirely possible to get sand/dirt/whatever in there, and have it remain even after washing.
When I travel by motorcycle (85% of the time), my phone goes in a ziplock bag as well, and then I put it in my backpack, or occasionally front left breast pocket of my jacket. I think if you are aware of the fact that you are carrying a $600+ device in your pocket, you can easily avoid scratches. All of the cases I use have a sufficient lip to set the phone face down, but I RARELY ever set them face down (grit/sand/etc can be so small and so easily scratch)
TL;DR-I've had great luck without a Screen Protector and prefer to run without them. Many have had the opposite and much prefer a SP for extra peace of mind. Do what you are comfortable with.