Been lurking here for a couple of months, and thought I'd comment on this one (maybe because I finally found a topic I actually know something about??!?!)
Candle snuffing is an excellent exercise that even beginners (one month or more experience) may use to develop control of the end of their sword. The proper motion required to snuff a candle includes speed, power, control of the exact location of the stopping point of the tip of the sword (centimeters directly over the wick), and most importantly, an abrupt stop of the sword's motion (i.e., no 'bounce'). This is one of several belt test requirements in haidong gumdo, where additional candles (requiring additional power and control) are added each test (so, one candle must be extinguished to achieve yellow belt, and six to achieve black).
For you Japanese sword pactitioners, candle snuffing requires development of te no uchi (coordination of proper motion of both hands with the sword).
If you have never tried candle snuffing, begin by placing a small feather on the floor (or tiny shreds of paper in a pile), and practice the cutting motion until you can reliably, repeatedly make the feather (or paper pieces) 'dance'. Candle snuffing is a good exercise for beginners through intermediate students, and is done with a wooden sword (bokken or mok gum).
Paper Cutting is another training technique appropriate for beginning to advanced students. I try to make sure students have opportunity to try at white belt, although I don't expect them to do well consistently until yellow belt.
Paper cutting is begun using a wooden sword - the tip (kissaki in Japanese arts?) is the part that actually does the cutting. Again, the technique requires proper control of the blade and proper cutting motion. In this exercise, the blade must be alligned correctly throughout the cutting motion, in order to cut rather than rip or merely hit the paper. Beginners are required to cut simple newspaper (cheap, available, easy to see the results), and I insist that students cut alongside (never on) an existing crease. Good cuts are clean enough to be able to see and address problems that need minor adjustments, such as when downward cuts tend to pull to the right or left, or when horizontal cuts do not stay horizontal). Newspaper is sufficient for practicing downward center cuts (from a stationary position, with the paper held at arms length by another student) and for horizontal cuts (hung 'clothesline' fashion over a string).
For more advanced paper cutting, I use longer paper. Butcher block, long rolls of craft paper, left-over wrapping paper rolls, etc., all work well. These rolls allow the use of longer paper sections, so holders may position the paper for diagonal cutting practice while maintaining a safe distance from the wooden sword and sword wielder. Thus, intermediate students may adjust/improve technique for diagonal cutting, while still using the wooden sword.
Live-blade paper cutting helps with blade allignment and control of distance, but requires additional safety precautions. Personally, I don't like to start anyone with live-blade paper cutting until about brown belt.
Fruit Cutting, in every case I've seen, is more for demonstration and 'Wow' factor than for actuall swordsmanship. It does help with eye-hand coordination, control of the blade, and demonstration of proper blade allignment in the cutting motion. I have heard of using dough balls and playdough as well, as these are less damaging to the blade. I have also heard (have not tried it personally) of using the wooden sword on playdough. I have allowed my beginning students to practice diagonal cuts with wooden swords on cucumbers and celery - it is crisp enough to show if a cut is alligned correctly by how the object breaks, and it's just plain fun for them to get to hit something.
Korean martial arts tend to have 'poom' grades (black belt 'junior' grades for younger-aged students). The 'poom' grades and ranks do not directly transfer when the student achieves a specifc age, but require additional testing and demonstration of maturity and proficiency. In these cases, I have seen haidong gumdo schools substitute tennis ball or ping pong ball hitting for bamboo cutting requirements. Rather than have an underaged student demonstrate proficiency by cutting with a live blade against hard targets, the student demonstrates control and precision against a stationary (suspended on a string) or a moving (thrown) target with the wooden sword.
Hope this helps.