Naturally, as the site grows, the number of votes of either kind goes up. The trend is shown below: upvotes per day in blue, 10*downvotes per day in red. (Multiplied by 10 to be roughly on the same scale). As you can see, recently the number of downvotes reached 10% of the number of upvotes.
For better readability, open the image in another tab.
The time interval is from the beginning of 2011 to December 1, 2013. Both graphs are smoothened by size 14 moving window (i.e., these are averages over 14 day periods).
Upon request, I added the chart with the ratio downvotes/upvotes for the same time period:
Sources of data: Upvotes per day and Downvotes per day.
Note: When interpreting the data, keep in mind that votes on deleted posts are not included in the SEDE database. Downvoted posts often get deleted: often by their owner, sometimes by other users, eventually by the Community bot (if there are no answers after a month). Also, some downvotes are removed after edits. The attrition of downvotes may partially explain why their number is higher in recent weeks than in the more distant past.
More charts To get a better look at the data, I broke the vote counts from the beginning of 2012 (not 2011 this time) by type of post: questions and answers. These are upvotes on questions (blue) and answers (red):
Answers are ahead, but both follow almost exactly the same pattern. The chart makes it clear that the number of upvotes is not keeping up with the ever increasing volume of posts. In particular, the all-time high was in the second quarter of 2013.
And these are downvotes on questions (blue) and answers (red):
Here questions are ahead, and the patterns are rather different. Both are at all-time high point right now, but for the questions the spike is much more prominent.