If you think about it, it's quite an obscure set-up, right? I mean, who thought to put two cymbals together to make the hi-hat? And when was it decided that the bass drum should go on the floor with a pedal to trigger it?
I think it's time to delve into the history of the Drum Kit...
B.D.K (Before Drum Kits)
In orchestras, percussion was (and is) generally performed by several people. Marching bands similarly assigned one person to each drum, allowing them to concentrate on their part and not collapse from exhaustion as a result of hauling an entire percussive ensemble on their backs.

When theatres were running low on money, they couldn't afford to pay quite so many musicians, so the percussionists were encouraged to multitask, playing the snare, bass drum and cymbals by hand.
In the 1890s, some bright sparks decided to put the bass drum on the floor, fashioning rudimentary pedals to trigger them, leaving their hands free for the cymbals and snare. It wasn't until 1909 when William Ludwig came along and made the pedal conventional.
Hi Hats, Tom Toms and Traps
1926 saw the first Hi-Hats appearing. Interestingly enough, they were originally called low-hats (no joke), being on the floor near the bass drum. They were later raised so they could be played by hand as well as by foot pedal.
Chinese Tom-Tom drums were added to the mix to create the conventional drum kit that would carry on through to the end of the century and beyond. The traditional kit then stood as a bass drum, a snare drum, 3 toms (two rack-mounted and one floor tom), a hi-hat and a crash cymbal.
The "Traps" were short for "contraptions" - whistles, klaxons and cowbells added to the kit to make them even more versatile. While the whistles and klaxons didn't become fully integrated, I'm sure you've heard your fair share of cowbells emanating from drum solos the world over.
As seen on TV
After Ringo Starr of The Beatles' fame played his Ludwig kit on TV in 1964, the popularity of the drum kit shot up exponentially. This is the point when rock bands started to take off left right and centre, with the percussionists emulating the famous drummer's set-up.
Mine's bigger than yours...
As is the nature of rock music, things grew more and more extravagant - double bass pedals were introduced for faster bass drum playing on heavier tunes. Ridiculous numbers of toms and cymbals were added for an as-before unseen amount of versatility from the kit.

And where to now? Well more recently, drummers have taken electronic percussion on board, with sample pads, triggers and laptops adorning their kits to integrate their live sound with programmed elements and even melodic ones, as sample pads can be used for any purpose.
I have no doubt the kit will continue to expand and evolve as technology does - perhaps the conventional drum kit will soon contain sample pads next to the hi-hat, or triggers on the toms.
We'll have to wait and see!