The Yamakasi do this (I believe). The idea is that when they train, they do as many reps of whatever as they normally would do, and then they do one more, for all the people who are injured or for whatever reason can't train. It's a nice idea; I like it because it helps create an attitude of perseverance and also helps build a sense of community.
Awww that's a caring thing to do for your team members. =D
Okay, after thoroughly reading Steve's workout routine guide, I realized that yes, going to failure is acceptable when working for endurance. That's what this is.
So, when you first start, go to your failure. Let's say, for example, you got 27. That's all you have to worry about this particular workout/training technique for that day.
Then, the next day, do 28. Again, that's all you have to worry about for this particular workout.
The day after that, do 29, and so on.
Even on a rest day it's still good to keep this up to help make sure you stay on track and constantly, slowly, progressively, push your limit.
Obviously, if you're doing other workouts/physical activity (and you should), two things could result from it.
1) Your muscles are tired because of the work you've done that day. If you don't make it to the number you're reaching... rest, try it later that day. If you don't make it at all the entire day, try that same number the next day, don't go up one.
2) You get stronger. If you realize 2-3 days in a row that, even though you're increasing the number by 1 every day, it's more than 1-2 reps from failure, it's a sign that you're not quite doing enough. So, the next day increase by 2 instead, and then if it feels like failure or 1 away from it, then you're back on track, and continue with 1 every day afterwards.
This is mainly an endurance-raising technique. But, like any work out, that doesn't mean that the strength gain switches off. It will still give somewhat of an increase in strength, too.
(Steve I need your clearance on this next statement)
If you were to do your exercise explosively (such as....let's say clap push-ups instead of push-ups, or jump squats instead of regular squats), it'll also add some power (fast twitch fibers) into it, while if you do it specifically slowly, it'll add to the slow twitch fibers more.
Hope this helps you guys. =D