Just counted my rifles, I have 24 Remingtons, and 13 each of the Mausers, and 5 Rugers (which includes 2 77/22s, 2 #3s, 1 77). I have others, also.
I have owned, bought and sold Remingtons now for just about 40 years. Yes, I had a broken bolt handle on a 788. Rifle was replaced free the next week. Yes, I have had broken extractors on 721s and 722s, none yet on 700s. Accuracy varied, from an out-of-the-box 40XB in .22-250 (back in the 70s) that came with a factory target of .105" (I never beat that, but got close) to a few that grouped about 2". I have had two 788s that would group consistantly under .1875" at 100 yards with almost anything that I put through them, much to the chagrin of quite a few other bench-resters with expensive rifles. I had a 721 in 30-06 that would group into .500" with most loads, factory or not. Never saw a Remington yet that wouldn't shoot at or close to 1 inch at 100 yards, although some took a bedding and trigger job to do it.
Rugers? I tried them when I was shooting bench-rest a lot, gave up after 5 of them. None of them (MKIs) would group consistently under 1" no matter what I did to them, but they are rock solid reliable and none ever broke bolt handles or extractors. The calibers I have in the single shots aren't that accurate (.45-70, .375 H&H), I don't try for sub minute groups out of them. Rugers are GREAT hunting rifles, but not target rifles. My current M77 is a 7.62x39mm, again not an accuracy cartridge.
The Mausers are various, some sporterized military, some pure military, some commercial. They are also fine hunting rifles, and again not target rifles, just EXTREMELY reliable.
I like to shoot, but I'm not much of a hunter, so having rifles that aren't 10,000% reliable doesn't panic me. If I hunted, and reliability were of more importance to me than accuracy, then I would choose a Ruger, a Mauser, a CZ, a Browning or a Winchester. If accuracy is the foremost consideration, then it would be a Remington every time. It seems to me that dangerous game does not require a superbly accurate rifle, so why not choose a rifle more suited for reliability? I mean, OK, a Remington might not be the worlds best safari rifle, but then again, neither is an Anchutz. Non-dangerous game? Yes, I wish Remingtons were more reliable, in my own experience reliability problems will become apparent at the range before the hunt, if you bother to go. If you haven't hunted with your rifle before, take a back-up, or be prepared to borrow one. I don't think Remingtons are any less reliable than other makes, percentage-wise, but since they make so many more rifles, there will of course be more broken ones. Not a higher percentage, just higher numbers.
I think that its sort of like this. There are three main characteristics in rifles that we all want. Great accuracy. 100% reliability. Low cost (at least relatively). Now pick which TWO characteristics you can live with. You can't have all three. At least, not 100% of the time from any manufacturer that most people can afford. Absolutely MUST have all three? Then be prepared to spend at least $1500 for the rifle (without scope or mounts), and more likely twice that, for a rifle GUARANTEED to have all three.
Has Remington quality gotten worse? Maybe. I haven't bought enough rifles made since 1993 to really judge that. I have only 6 that I can think of, and every one is flawless and groups under 1" at 100 yards with factory ammo (except my 700 Stainless, I have only shot handloads through it, no factory; it groups .500" or less). I'm not arguing that Remington quality hasn't gotten worse, only that I haven't seen it.
If I were a beginning rifleman, looking to buy my first high-powered deer rifle, how would I pick a rifle? I would realize that if I bought a Remington, it would MOST LIKELY shoot well, but it MIGHT have a reliability issue. I would realize that if I bought a Ruger, it would PROBABLY be 100% reliable, but it MIGHT not be as accurate as a Remington, but still quite adequate for hunting. Each and every brand of rifle has its strong points and its weak points, few are outright turkeys. People have their preferences, and their pet peeves. You are quite free to develop your own, but please don't think that you are an expert on any particular make of rifle because you owned one and it was a turkey. And just because someone like me that has had a certain brand for years and likes them, doesn't make me the final authority. That is what makes this sport so interesting, there is enough room for all of us, for all of our opinions, for all of our likes and dislikes. Go to the store (or your friends' houses), find what YOU like and buy it. Live with it for a while. Develop your own opinion based on experience, go from there.