This is pretty well established knowledge right now. I'll list everything pertinent about lithium ion batteries and charging smartphones:
Edit: Note that I mention Lithium Ion in this post, but the HTC One uses Lithium Polymer. They are for all intents and purposes equal in terms of their usability, except for slightly less charge cycles
Edit 2: Hello Reddit! No idea this would have taken off. I'm "coolmatty" on reddit. This is an overall generalization, and there are plenty of resources that go into more detail. Places like Battery University are great sites to start.
1. Charging is what reduces the life of a lithium ion battery. Batteries are usually rated between 700-1000 charge cycles while keeping 90% of their capacity.
2. Charging 0-100% counts as one cycle. Charging 80-100% 5 times counts as one cycle.
3. Leaving your phone on the charger after it is charged has the potential to reduce battery life, although this is less of a problem with newer devices as they often disconnect the charging circuit until the battery drops below ~95%. Generally only an issue if you leave it on the charger for 24+ hours.
4. Lithium ion batteries do not require any conditioning.
5. Most lithium ion devices arrive with ~40-50% battery life remaining, because this is the optimal charge level to store a lithium battery for long periods (such as sitting on a store shelf for months).
6. Slower charging maintains the battery's overall lifetime capacity better than fast charging. This is likely why the HTC One does not have Qualcomm's Quick Charge enabled. It's debateable whether you'd notice the effects over the typical lifetime of a smartphone, however (2 years).
7. Not exactly related to lithium but just in general: smartphones (and tablets, etc) have charging circuits that only draw a certain amount of amps regardless of the number of amps the charger provides. Using a 3.1 amp (tablet-level) charger is not going to significantly increase the speed at which your phone charges. Most phones only use between 0.8 - 1.2 amps. Anything over that is overkill.
8. Storing a lithium ion battery at 0% is really bad for its lifetime capacity. Running it to 0% generally isn't recommended all the time, but a few instances won't hurt it.
9. Recharging from 0-100 doesn't make your battery run longer. It can, however, reset Android's battery level stats so that it can more accurately state the battery level.
10. Charging from ~95% to 100% takes a long time because it must do a trickle charge. Maxing out the battery like this can reduce overall lifetime capacity, but generally not enough to matter. You'll see this impact more often in larger applications of lithium batteries (like cars).