My concern in general, especially for the folks asking what basic gear should they slim down to, is that it might not just hurt, it might kill. I am very comfortable with my skills in the woods, thou the last few years I have found a lot of more knowledgable people out there doing this in a much smarter when then the way I had been, but I have been in and around the woods solo for 38 years now. But as comfortable as I am out in the woods, I am surely not going to recommend to anyone not to carry the basics. Why would you? We are after all talking about someone asking a question, and while you probably answered honestly, would you tell that to anyone? Without knowing their skillset?
And I am not saying that someone couldnt make it with the gear, I am saying should they? Yes I can make a fire without a MagStick or firesteel. Do I want to if I am injured and alone in the woods of the beaten path? Nope. I can make it without a FAK, do I want to out in the bush? Nope.
People like Les Stroud, Allen "Bow" Beauchamp, Doug Ritter, Ron Hood, Jeff Randall, the list goes on and on.... all recommend a basic degree of equipment be carried when heading out.
Well, dying most often hurts, though not always. So I'd kinda bunch the whole dying thing in with being hurt to various degrees.
I didn't read the opening post as asking what he should carry at minimum, though. I read it like he wrote it. He asked what would be the minimum gear I would take along on a day hike or an overnight, and I replied. I dislike lying, especially when I have no sensible reason to lie.
So, why would I lie about what I would carry as a minimum? For someone's safety? Whose? If someone is willing to chance their life on the words of a guy on the Internet that they've never seen in person and don't know even by name, then perhaps it would not be cruel and unrealistic to suggest that the premature, accidental death of that someone is a statistical certainty and cannot be avoided even by the soundest of advice. So, yes, I would, and did, tell what I consider to be my minimum gear for simple day hikes or overnights in familiar terrain. I'm not going to lie about my thoughts for the safety of the general public. If I went on that road, soon I'd have to start proclaiming that knives without guards and folders without locks are fatal instruments of death that no reasonable human should ever use, lest they risk their safety and that of their loved ones in most horrifying ways.
I'm not recommending people to not carry "basic" gear. I'm recommending carrying whatever they feel is right for them. On top of that, I only suggest, for those who consider themselves experienced and reasonably skilled and who are interested in such things, to occasionally try going with pretty much nothing except clothes in familiar terrain. It's not something you should do if you feel like you're going to hurt yourself, or if you feel terrified at the thought. It is, though, something that will certainly feel different and may prove a great experience and a valuable lesson.
I'm not saying that people should always make do with minimal gear. I'm saying that it would be very good if they had skills enough so that they
could, if the situation calls for it. And that's hard to achieve without actually practicing it. Which brings me to this post by Khalnath..
The gear people choose to carry in the bush is totally personal, but IMO, no matter what else you carry, if you don't have some kind of edged tool and a source of ignition, you are not prepared.
With a knife or hatchet you can make a fire and shelter, and with that you should be able to make do. If you don't have a knife, how do you expect to make shelter if you are stranded? IMO you should even carry more than that at the minimum, like some tinder, plastic sheeting, and cordage.
Seriously, there is such a thing as "minimalist", but it is a different matter from "unprepared", no matter what level of skill you have. SAR techs go missing sometimes even when they ARE prepared. I am no expert, I won't tell you what I think you need to survive in the bush... but you definitely need more than day clothes and your bare hands.
Prepared is a matter of opinion, of course. I'll chime in with mine. I can make fire without a knife or a hatchet, in a number of weather conditions over here where I'm "at home" and familiar with the terrain and weather. I can certainly make shelter without anything beyond my bare hands in the way of tools. Actually, I find it amazing that someone could think it impossible or near so to build shelter without a knife. I mean, you do have your hands, do you not? You can use them for all kinds of things, from breaking some nice conifer branches to plain digging in snow or soft earth, or making a quick tool for the task. Sure, I couldn't build a log cabin with my bare hands, but then, my idea of shelter isn't as lofty as that. And besides, your most important shelter should always be your clothes. If you've chosen them right, you should be able to survive for prolonged periods of time in your present environment without fire or any further shelter. So, don't choose them wrong, and you'll save yourself a lot of work.
And fire, what do we need fire for? For cooking, certainly, or warming or drying. But if you've brought the right kind of food or are not staying long, why should you need to cook at the fire? If you've brought the right clothes, why should you need to warm up? Indeed.
The most revealing sentence of all, though, was this: "I am no expert, I won't tell you what I think you need to survive in the bush... but you definitely need more than day clothes and your bare hands."
That, my friends, is the modern, urban man speaking. The man who has been, perhaps by no fault of his own because his parents took his choice from him, so violently cut from his natural environment that he doesn't understand it quite as he should anymore.
If we - humans - really absolutely needed more than clothes and bare hands to survive in the bush, then we would not be having this discussion, because the human race would have been wiped out before our little civilization got started. Because, you know, we're not born with computers and knives and cars and television sets. It took a long time for man to invent anything that could be claimed to resemble a modern knife, or even fire. And still man survived. If it was impossible to do, then we wouldn't be here today.
I mean no offense with that - it's simply something to think about. Man conquered the world with his mind and hands, and made all else that he could use with those two things. That's the bottom line, because history says so.
Phew, that was long. Sorry about that, guys. I'm just trying, and likely not succeeding very well, to explain my original reply. I didn't think it would be considered a recommendation, as the original question was about our (that is to say yours and mine and everyone else's) individual minimum gear choices. Didn't think answering a question honestly would turn into a national security issue.
) The pizza didn't freeze! 
