Imagine your life as a film. Add all the stuff you know.
Is it possible to express this amount of data in bits? (A rough order of magnitude would be ok.)
This is a tough question, and there's a few routes to go. When we are watching this life played back, do we want to be able to go to any arbitrary moment and observe what was happening, or do we only want to watch life as we watch it? This would be the difference between recording all information that bombards our brain, or just the information that we are attending to.
We'll go with the first one, as this will be easier.
I'm going to ignore 'thoughts', and just look at information as it enters the body.
We need to know a couple things before we start.
What is the data rate of our eyes? What is the data rate of our ears?
As these are our most dominant senses, if we want a few orders of magnitude for information, we will get it from these two.
Researchers at the University of Pennsylvania School of Medicine say that the data rate for the eye is about 10 million bits per second, or about 1.25 Mb/s.
Our eyes have about 120 million cells, and they sample at roughly 30 Hz. Determining the number of 'bits' is hard, as eyes have a nonlinear response, so the amount of information they are transmitting is dependent on what the cells are observing. I will trust their number.
As vision is our most powerful sense, and accounts for over 40% of the processing in our brain, we know that the majority of the information will be from the eyes. (EDIT: This is incorrect, see the data below.)
Now onto the ears - our ears can hear up to about 20 KHz, and to actually pick up these sounds we need to sample at twice that frequency, or 40 KHz. That doesn't tell us how much information we actually get though. This question on Yahoo! Answers goes a little bit deeper, specifying that ears cannot distinguish information that is represented in more than 16 bits.
This is kind of an interesting way to determine the sensitivity of our ears, as we don't have to wonder 'well, how well can I distinguish what I hear?', rather the question is 'We have these samples of audio, and people can't hear the difference between them, therefore our ears cannot transmit this much information'.
So we have eyes and ears, and we now need to do some math.
I'm going to assume all these rates are fixed, the actual information that is transmitted is nonlinear as the spike trains from our cells change depending on what they are sensing.
I wrote a little python program, available here.
Now this sounds a little silly, do our ears really transmit more information than our eyes? Actually yes, because they are sampled so much more frequently. The eyes sample at roughly 30 Hz, whereas the ears sample at 44 KHz.
This analysis ignores the number of cells, and is likely incorrect for a number of reasons. We ignore the other senses, as well as information being sent between brain regions (processing of information).
This question brings up an interesting point though, the raw information that we receive is meaningless, only through successive iterations of information abstraction (what neural networks do, they operate on regions of information, gaining a higher and higher level picture) can we begin to distinguish the world as it is. When we see something, we can immediately break the world apart into segments, we know what can move, we know where things are, we know when we put them there. This isn't information that we were given at our current place in time, it's rules that we have learned about what we see in the world through a lifetime.
Additional source of information: How many colors and shades can the human eye distinguish in a single scene? This Photography.SE question goes into logic about how much information we can discern, more closely matching the analysis on the Ears, rather than the research data that we used.