In 1995, 6.7% of Americans were on the Internet. That percentage exploded to nearly 60% by the end of 2000. I ran regressions on the slowdown of Church growth against the percentage of people in American and in the world who are on the Internet. The proliferation of the Internet doesn't appear to be a significant factor of the declining church growth in the 90's--the slowdown in growth started before most people had even heard of the Internet, and the slowdown did not accelerate when the popularity of the Internet mushroomed.
I think once we conder several other factors, the traditional theory about the internet having a negative affect on the Church will be well supported. For one, it isn't enough to simply add up annual missionary numbers along with convert baptisms, during the years the internet was booming. Roger makes a good point that growth rates had already been on the gradual decline just before the Internet took off, but there are good reasons why that was so. Instead of using gross convert baptisms figures, I think using a "converts per missionary" (since the size of the missionary force goes up and down) stat is a more reliable metric when trying to ascertain the level of success the Church has in converting others. So consider the following chart:

During most of the 80's the baptisms per missionary figures were fairly stable, fluctuating between 6.6 and 7.1 baptisms per missionary. Between 1980 and 1986 the number of missions worldwide increased by only five. However between 1987 and 1989 there were 34 new missions created. In 1990 alone, the Church created another 28 missions. So between 1986 and 1990, the Church went from 193 missions to 256 (any discrepancy in the math is due to the closing of other missions).
Now in the chart you can see a boom in baptisms per missionary in 1989 and 1990, each year yielding over 8 baptisms per missionary. The reason for this is not due so much to the increase of missions, but rather where those missions are built. Particularly in poorer countries with where baptisms are easier to come by, and the people are generally divorced from most forms of mass communication (i.e. information). Also, keep in mind that a large number of missions created in any particular year will not yield a large number of converts that same year. It generally takes a at least a year or two for missions to get organized, create a conversion base, and gradually use those conversions for future member referrals (most converts are member referrals).
So my argument is that the boom in conversion efficiency between 1989-1990 was probably a result of a serious increase in missions created in countries that traditionally see higher rates of conversions. Countries that have a very high rate of conversion are generally third world countries, particularly anywhere in Latin/South America and the Polynesian Islands (Phillipines, New Zealand -places where internet access is more scarce)
So for instance, in 1981 and 1988 the Church only saw a net increase of 34 missions, and of those missions created only 20% were Stateside missions. More than 45% of those missions were based in Latin American countries, and 27% were based in either the Phillipines or Africa. Only 8% of them were based in Europe, which has the worst conversion rates in the world.
So after planting these seeds in countires with a high yield, the average missionary saw a higher production in 1989 and 1990. The next interesting thing we see is a dramatic drop in 1991-1992, and I think we can safely attribute this to the fall of the Berlin wall which opened up mission opportunities the Church never before had. So in 1990, for instance, 32% of the 28 new missions were based in Europe. The problem here is that Europe, especially Eastern Europe, is an extremely difficult place to gain converts. So with 11 New missions to Europe, along with a new one to an equally difficult Japan, the church would naturally see a drop in conversion rates.
So what we see next is a gradual leveling off in production rates up until 1994. And even though the missions increased between 1991 and 1994, we begin to see the final downturn of the Church's growth rates in 1995. Between 1991-94, 7 of those missions would be to Russia and 11 would be to Europe (both areas with extremely low conversion rates), however the Church would offset that loss in production by building a whopping 31 missions in Latin America, 8 to the Polynesian Islands, and 9 to Africa, all of which are third world countries with much higher conversion rates. So this I believe explains why teh figures saw a slight rebound and leveling off between 1992-1994.
Now this brings to the "big dive of 1995" which obviously corresponds to the era and rage of the Internet, along with the birth and popularity of Windows 95. I don't think this is just a coincidence. Roger said by the year 2000 60% of Americans were on the internet, and I think we can safely say that figure rose each year after that. So what the Church saw from 1995 and on was a miserable decline with no end in sight. What was a baptism per missionary rate of 6.35, become 6.25, which became 6.07 the following year, and then 5.62, and then 5.17, and then 5.22 and by the year 2000 missionaries were only averaging 4.5 baptisms. Eventually, the rate hit an all time low in 2003 at 4.31 baptisms per missionary.
Now the Church is essentially a corporate structure that plays by corporate rules, so they have their teams doing their analyses trying to figure out how to offset the decline in business. So I don't think it is any surprise to see what the follow chart tells us, which probably explains the slight improvement in 1999:

As you can see the Church started cutting way down on its funding for newer missions, and it is very selective in where they place them. Since 2003, 71% of all new missions have been opened in third world countries, only 1 in Europe and 2 in Japan. This is probably what accounts for the slight improvement in conversion rates for 2006-2007 as well.
In 2008 the Church had a net increase of ZERO missions, and in 2009 its net increase was -4! That's right, the graph wasn't a mistake for that year. In 2007 the Church had 348 missions and in 2009 it had 344, and the only mission that I know of being created in 2010 is one in Nicaragua.
If we can't attribute this to the massive dissemination of information, then what else can explain it? I see teh church fighting an uphill battle, treating spiritual conversions like a commodity that has to be won using coporate techniques. Throwing money at certain areas to offset losses and meet production goals.
Anyway, I look forward to some feedback...