How come firearms, which took precious time to reload, replaced bow and arrows which could be fired off in a more rapid succession?
The biggest advantage guns have over archery is ease of use. A proper war archer can take 10 years to train properly, training a arquebusier can take a few months. Notably, the Ottomans continued to use composite bowmen even after Europe had made the switch to guns. In the Battle of Lepanto in 1571, a huge number of the Ottoman bowmen were killed in the naval defeat of the Ottomans. Some historians argue that this was a major blow to the traditional mode of Ottoman warfare.
Another big advantage of guns was in armor penetration. As guns became more common, armor underwent a significant change. In some cases, the thickness of breast plates tripled from 1mm to 3mm in order to bullet proof the armor. To compensate for the increased weight, the coverage of the armor was reduced, starting with the boots, then moving to the upper legs, then upper arms.
Source: Weapons and warfare in renaissance europe. You question is one of the major topics of this book.
If I am correct, your asking about any time period before the American civil war, forgive me if I am assuming incorrectly.
Armor. An English longbowman had a "killing Range" of around 20 meters, past this point, it was unlikely the average arrow could penetrate a knights full plate armor. A bullet was much more likely to cause damage past that 20 meter range.
When fire arms came into the field of battle, this did not immediately put the bow or crossbow on the back burner, armies would be equipped with both troops who used bows/crossbows and some who would use firearms.
It is also important to note that even after things such as mortars and cannons were introduced on the battlefield, Hand to hand combat still occurred as did battles that utilized bowmen.
Greater History has some great episodes about medieval combat arms and how they came to be and how they were used. I highly reccommend checking out the episode on English longbow: http://www.youtube.com/watch?v=geNG-Ot40W0&list=UUrPyMDvVQOF5QaX3fHiLOqA&feature=share&index=2
And The episode on The Sword which covers battles where cannons were common place but archers and Sword to Sword combat was still used: http://youtu.be/1SijLXKmlsw
This question was recently addressed very thoroughly here: http://www.reddit.com/r/AskHistorians/comments/1x03jt/if_early_guns_were_so_inaccurate_and_took_so_long/