The late George Flynn published in 1995 (and subsequently updated through 1999) Hugo Voting: Let’s Look at the Record (Again), an exhaustive compilation of the number of Hugo Award nominating and final ballots cast in the years 1971-1999. Regrettably, nobody has continued that table as far as I know, and surprisingly, the figures we have on hand, including a number of Hugo Administrator reports, don't include the nominating and final-ballot counts. (Some of them only include the counts per category, which doesn't tell us how many total ballots were cast.)
There are claims that "Puppygate" is the only reason Hugo nominating and voting numbers are on the rise, and that prior to the arrival of the Puppies (apparently in 2013), only a couple hundred people were nominating. Well, it's true that interest in the Hugo Awards reached something of a nadir in 2006, when, despite being one of the larger Worldcons (Anaheim), only around 500 people nominated. The following year, WSFS (through the Mark Protection Committee) set up what is now known as the Hugo Awards Marketing Committee and established the Hugo Awards web site. I've gone back through what figures I can find and accumulated below the number of nominations per year from 2005 through 2015.
In the list below, "at least" is the count of the most-popular category. The total number of ballots was higher, but we don't know how much higher. It has only been recently that standard reports have included the gross number of nominating and final ballots cast in the reports.
2000: No data available
2001: 495 (539 total; 44 invalid) (Change from 1999: 0% — there were 499 nominating ballots in 1999)
2002: At least 486 (Change from 2002: -2%)
2003: 738 (Change from 2002: +52%)
2004: At least 462 (Change from 2003: -37%)
2005: 546 (Change from 2004: +18%)
2006: At least 430 (Change from 2005: -21%)
2007: (Not able to ascertain from reports)
In 2007, WSFS established the Hugo Awards Marketing Committee and launched the Hugo Awards web site.
(ETA: Per comments, 2008 was the first time that a Hugo Voter Packet of finalist works was available to Worldcon members. It was organized by John Scalzi in 2008 and 2009.)
2008: 483 (Change from 2006: +12%)
2009: At least 639 (Change from 2008: +32%)
(ETA: Worldcons began organizing the Hugo Voter Packet directly starting in 2010.)
2010: 1094 (Change from 2009: +71% Note that this was in Australia and followed a Worldcon in Canada; as a percentage of eligible members, it was a vast increase year-over-year)
2011: 1006 (Change from 2010: -8%)
2012: 1101 (Change from 2011: +9%)
As I understand it, the first Puppy campaign started in 2013.
2013: 1343 (Change from 2012: +22%)
2014: 1923 (Change from 2013: +43%)
2015: 2122 (Change from 2014: +10%)
There's no doubt that Puppygate caused a big spike in participation (and it will be a huge spike in 2016, I expect, given all of the people who joined after the nominations were announced last year and who are all eligible to nominate this year); however, we were seeing a slow, steady increase from 2008 (the first year after we established the Marketing committee) through 2012, amounting to a cumulative 225% rise in participation (admittedly from a small base), and I'm fairly confident that the trend would have continued with or without the participation of any particular partisan group.