I trained in a couple of different martial arts for several years before beginning aikido (kenpo and tai chi), and my perspective is different than some of the others expressed in this thread. In kenpo, which can be considered an extremely devasting and lethal art, it was very much frowned upon in our school to hurt your partner, even during sparring class. There was a great deal of emphasis on the use of control in applying techniques and during sparring class. Granted, I did occasionally get injured, but it was usually from a beginning student who didn't have the proper level of control or attitude during practice (one of these was actually a 10 year old who unintentionally cracked one of my ribs with a kick when I was initially teaching him a technique - definitely a control issue!).
Regarding falling, my experience was that very little emphasis was placed on falling, although we did practice some techniques that were almost identicle to koshinage and aikitoshi. Basically, we slapped out on those falls, without the emphasis on any rolling or smoothing out the fall. Of course, years later when I began aikido, I had completely forgotten how to take those falls and had to learn them all over again. At least this time it was on a tatami instead of a hard floor!
Regarding falling on concrete - following a recent seminar after we finished cleaning up the mats in the gymnasium, one of my fellow students dared our sempai with the best ukemi in our dojo (and that I've ever seen) to take a high breakfall on the wooden gym floor. After a few moments of contemplation, the sempai politely declined, saying he'd done it before and it was too uncomfortable.