Why is English written and read from left-to-right as opposed to right-to-left, top-to-bottom, or (not even sure any language does this) bottom-to-top?
Writing in English was derived from writing in Latin (it's mostly the same alphabet, after all), which in turn was derived from writing in Greek — which was written from left to right. So this is why all European writing systems go from left to right: because they're derived from Greek.
But why did the Greeks write from left to right? I'm not sure. They adopted their alphabet from Phoenician (or, if you wish, Proto-Canaanite), which was actually mostly written right to left (and sometimes boustrophedonically: direction alternates every line, so that each line starts just below where the previous line ends). In fact, Greek used to write from right to left for a while, before they switched to left-to-right.
Another derivative from Proto-Canaanite was Aramaic, from which Hebrew, Arabic, Persian etc. are derived, and they're all still written right-to-left. It is also believed that Brahmi (the family of Indic scripts) was derived from Aramaic and was written right-to-left for a while, before switching to left-to-right.
Why did this switch happen, in Greek and Brahmi? According to a theory mentioned on Wikipedia without a citation (so it may just be an urban legend),
Many languages that existed before the invention of ink were written right to left since this is the more natural for right handed people to hold a chisel in the left hand and the hammer in the right. After ink became the main method of writing, writing from left to right became preferable since it avoided smudging the ink.
Make of that what you will. It is known that Chinese, Japanese and Korean are written in vertical columns going from top to bottom and ordered right to left because it "facilitated writing with a brush in the right hand while continually unrolling the sheet of paper or scroll with the left". (The Chinese invented paper, after all.) So there may be merit to the explanation quoted above, that the medium influenced the writing direction.
English writing, like almost all alphabetic scripts used today, ultimately derives from a Phoenician alphabet used around 3000 years ago. The direction of writing was variable early on - some texts are written in boustrophedon, "as the ox ploughs", which means that alternate lines are written in opposite directions. At some point Greek script settled down to left-to-right, and all the European scripts which derive from it (Latin (i.e. English), Cyrillic, Georgian, Armenian) adopted this pattern. Most middle-eastern scripts (eg Hebrew, Arabic, Aramaic) settled down to right-to-left. Descendants further out (eg Indian and south-east Asian scripts, and also African scripts such as Amharic) are mostly left-to-right.
Nobody really knows why particular scripts settled in particular directions; but it has often been remarked that left-to-right is easier for right-handed scribes using pen and ink, because there is less chance of smudging what you have already written.