That's right, it was simply a series of 15 moves every hour. Our chess club had one of the early chess clocks made by Wilson, called a nodding clock.
Why do people play without increments?
In my somewhat limited recent blitz experience, people used clocks with increment features, but stuck with a pure 5/0 time control anyway.
They seemed to prefer the game to be shorter and didn't mind time scrambles.
Personally I prefer to play with an increment.
Maybe some avoid increments because the clock interfaces are unwieldy.
The Chronos interface is one of the worst I've ever seen anywhere.
According to chessgames.com, the very first chess tournament ever played with clocks had time added on per moves. So that guy who said "in the old days the clocks were different" is either mistaken or missing the point.
http://www.chessgames.com/perl/chesscollection?cid=1012412
Increments make a lot of sense.
The article that you mentioned doesn't say anything about "time added on per moves." Those sorts of time controls weren't invented until Fischer developed the Fischer clock, right?
No. You sound like you're intentionally misunderstanding me so I think I'll leave it at that.
Basically, increments are completely pointless. If you use a nominal increment like 2 seconds per move, all you are likely to get is a protracted time scramble with both sides making "nothing moves" and hoping the opponent actually makes the mistake of trying to think. If you use a larger increment like 15 seconds per move, you may as well just add ten minutes onto the time to start with. It's completely pointless and only serves to massage technology fetishists' idea of fun.
The main effect is that it makes the game a bit like "buzzer chess", where you have to move on the buzzer every ten seconds. If I'm playing a fifteen minute game, I might want to use five minutes over a single move, which would put me in time pressure if large increments on a small time-base were employed. So they remove the option of a long think, which is unnecessarily limiting and which suits people who play somewhat mechanically. Therefore, increments are a completely unnecessary imposition on other players for the sake of some people's egos or worse. They add absolutely nothing. Fischer has a lot to answer for in this respect.
I like increments in longer games, but not in shorter games. in shorter games, it just means move as fast as you can so your opponent, who is actually thinking, will lose on time. In longer games, it means you get at least x amount of seconds to think before you actually start cutting into your time. so in a 15|10 game, you can take your opening moves very quickly, get about a minute of extra time (at least that's what i usually end up with around move 10), then take your time to think the rest of your moves through thouroghly, without having to stress too much about the clock.
Can people justify this way of playing?
Seems like for any really long game (lots of moves) it'll be just a race for time. Even a 2 second increment can at least mean you don't lose when you're two queens up.
A better question is 'why do people play with increments?'. It seems rather arbitrary to me, and makes a little more sense to have a set amount of time for the game and that's IT, instead of oddly giving people extra time on every move.
Increments do add some good things to the game . 1) The outcome of the game is more often a proper outcome and not decided by the clock . 2) having complete scoresheets to ALL your games is a plus imo , but maybe not everyone's . 3) they pretty much eliminate mad time scrambles at the end of games
A five or more second "delay" (which is quite common now in USCF Game in 30, and Game in 60) can save you from nutty time scrambles.
Additionally, endgame knowledge allows you to convert winning endgames (rapidly), whenever you're using a delay or an increment. Without increments, many times you'll be SOL, shite out of luck.
Without delays or increments, USCF Quick Chess time controls start to feel like online Blitz, or even Bullet. Great if you younger than 27 years. Hell on the nerves, if you're older. 
Typically, in USCF OTB, you don't have to keep score, if your clock has less than 5 minutes remaining.
So even in a 5 hour game, the increment can prove very helpful in completing the game, on the board, not the clock.
In USCF play if either player gets under 5 minutes left on the clock BOTH players are allowed to stop keeping score ... this differs from FIDE ( when increments arent in use ) you can only stop keeping score when your clock has less than 5 min left , which is more logical to me .
About #29: that wouldn't happen with the Bronstein clock. I find it more accomplished than the Fischer one.
Why not learn to manage your time so you always have either more time than your opponent or a very clear plan of how to play your moves very quickly? The number of games I've won because I've converted a complex early middle game and a time deficit to a positional advantage, which then converts to a time advantage, which then converts to a tactical advantage, which converts back to a big time advantage when it really counts, is because I have deliberately managed my time so as to bring that about and, hopefully, mess with my opponent's mind. People who need increments are people who can't manage their time and the only advantage is a complete score sheet. It's even a fallacy to say that the game is won on the board, when the standard of play drops because of lack of time.
I agree with you. Having an increment really helps. That's why I rarely play 30|0 time control in chess.com.
I always play 15|10 time control, so I can spend time the rest of the game, and if it comes to a winning endgame for me, I play fast and gain time on the clock.
On the other hand, if it's a winning endgame for him, I am probably going to lose anyway, and instead of playing fast I just resign.
The only problem is if the game is if I'm still in an unclear and complex endgame position even after 50-60 moves. Then, I will have very little time on my clock, and I will have to play each move within 10-20 seconds, even though it's a complicated game. However, the same thing goes for my opponent too, so I guess it's not a great problem, as long as one side eventually breaks through.
However, whatever way the game ends, it will still be a better quality game with an increment than without one, for if you don't have an increment, and you reach a complex endgame, it will just become a time struggle, resulting in huge blunders.
So, if you want a better quality game, play with increment.

According to chessgames.com, the very first chess tournament ever played with clocks had time added on per moves. So that guy who said "in the old days the clocks were different" is either mistaken or missing the point.
http://www.chessgames.com/perl/chesscollection?cid=1012412
Increments make a lot of sense.
The article that you mentioned doesn't say anything about "time added on per moves." Those sorts of time controls weren't invented until Fischer developed the Fischer clock, right?
http://en.wikipedia.org/wiki/Game_clock