It won't have any effect at all, not even a minor one. Trust me; I've been a "battery hobbyist" for nearly a decade now. Lithium-Polymer and Lithium Ion batteries have no memory effect whatsoever; these warnings and advice that you're reading are a carryover from previous battery chemistries where it was good to be do several full drain/recharge cycles.
Lithium Ion, in fact, is actually very bad to do a full discharge and it will reduce the capacity of your battery. 4.2v is full charge for lithium ion/Lithium Polymer, and there is a protection circuit built into the battery somewhere around 2.4-2.7v. Once that threshold of discharge is reached, the battery will cut itself off to prevent even worse damage. This is why sometimes a phone will have trouble turning back on after the battery totally dies - the battery has to be recharged past the cutoff threshold before the phone will start up again. This is the point where you have "0%" battery life left on the phone. It's much better to charge your phone frequently than to do full charges and discharges - it will keep your battery in much better shape.
Other than avoiding full drains, the other thing you should do is to only use high quality chargers. Now it won't matter much if you charge the battery in your phone as the charging algorithms are software controlled in the phone itself, but I would be very wary of using ebay wall chargers for the loose or extra batteries. Lithium Ion gets damaged if charged past 4.2-4.25 volts, and becomes an explosion risk should the internal vents fail. The problem with many cheap chargers is that they continue to slowly trickle charge past 4.2v, so you'll be fine if you use a DMM to check the voltage of the batttery every ten or so minutes, but if you don't it will slowly rise to 4.21, 4.22, 4.23v. If you leave it overnight you very well may end up coming back to an overcharged battery that is not only holding reduced capacity from the damage, but is a safety risk as well. I even go so far as to have special hobby chargers with perfect algorithms to charge my loose lithium ion cells for my flashlights!