For many years, astronomers estimated there were about 100-200 billion galaxies in the universe. However, new research gleaned from the Hubble Space Telescope shows that 100-200 billion is about 10 TIMES too low of an estimate. The research group, led by Dr. Christopher Conselice, used a mix of new deep-space images and previously published data to make updated measurements of the number of possible galaxies a different points in the entire history of the universe [almost 14 billion years]. Link
With the additional help of mathematical models, the research group was able to basically prove that the number of galaxies we can account for do not make up the entirety of the universe. In fact, there may be galaxies either too faint and/or too far away to be seen with today's technology.
What does that mean? Well there is likely at least 1 trillion galaxies...and maybe even 2 million, if you're going on the high end of the spectrum.
Dr. Conselice said in a NASA news release, "Who knows wha interesting properties we will find when we discover these galaxies with future generations of telescopes?"
But when will that be?
Well, there's a soon-to-be released one  that might show of these galaxies that we were previously unable t see. It is called the James Webb Space Telescope. This next generation telescope will allow for whole new levels of resolution and sensitivity from long-wavelength visible light through near/mid-infrared light. One particular goal for this new telescope is observing some of the most distant events and objects in the new universe, like the formation of the first galaxies! Not to mention the ability to better understand the formation of stars, planets, and direct imaging of exoplanets.
The image above is from Flickr user Mooglet's account and is licensed under creative commons.