Part of the interesting issue with your question is that "trash" was not really a concept prior to industrialization. A sketch is given here (PDF) with the straightforward argument that "Trash has always been a product of sorting, and what counts as trash depends on who is doing the counting." This is taken directly from Susan Strasser's Waste and Want: A Social History of Trash who herself cites such examples as "the 1835 edition of The American Frugal Housewife, explaining how to sort food waste...'to see that nothing is thrown to the pigs which should have been in the grease-pot.'" Strasser uses this as a way to make an argument about urbanization and the advent of social classes, but that's not relevant to your question.

If, instead, you simply want to know what "waste" people had to get rid of--an important difference because of the aforementioned class connotations of "trash"--you'll have to clarify what what time frame you're curious about. The PDF I linked to gives a good summation of the recyclability of things we might consider throwing out today, stating "When an item was of no further use, Yankee and Jewish peddlers collected paper, rags, rubber, bones, hides, and metal from households, in trade for needed sale items." Which leaves not a great deal for waste, perhaps; The study linked to at Upstream gives the breakdown:

"Ashes (mostly coal ash from furnaces), garbage (mostly food scraps), and rubbish (miscellaneous products such as paper, old clothes and the like)...75 percent (955 lbs) was ashes, 15 percent (187 lbs) was garbage, and 8 percent (92 lbs) was rubbish."

Keep in mind this is the breakdown given by a 1906 paper about New York waste which the Upstream study cites.

Of course, there's also the infamous human waste aspect of pre-industrial waste. Since plumbing wasn't wide-spread--non-existent, depending how far back you're interested in--human waste, well, "By the mid-1700s, American households, to a limited extent, began digging refuse pits for disposal of their household wastes, rather than throwing the garbage into the streets and alleys." Basically, open air cesspits combined.

All this being said, the big issue is what time period you're curious about. Keep in mind I'm not a professional historian and I'm sure someone will have something to add or correct regarding this.