Taking raw temperature data from the Global Historical Climatology Network (GHCN-Monthly) data base, we can plot average temperatures taken from ground stations over the previous three centuries. I took all the data from all weather stations in all countries and averaged the temperature values per month. Plotting each month separately you get the following graphs.

Then to get a better idea of what's going on overall I calculated the average global temperature per year, and with minimum amd maximum values.

Assuming that the original data is good, and you can find descriptions of how it was collected on the GHCN site, the results seem pretty clear. Over the last three centuries there has been a steady rise in average global temperatures. However, no recent exponential trend is evident. Instead this looks more or less like a linear increase, with the slope beginning before the industrial revolution gets into high gear in the 19th century. The overall average graph (blue line) in the above image shows this best, and I can hold a ruler up to the screen and get a pretty good fit.
The good, the bad and the inconvenient
So the bad news is that after even a cursory examination of the data we can clearly see that global warming is a real phenomena rather than merely a PR stunt or something else which was invented by Al Gore. However, the good news is that this doesn't appear to be significantly related to human activities - despite our inflated sense of self importance as a species. If the warming were primarily due to industrial activity I would expect to see a significant deviation upwards, approximately half way along the graph as factories multiply and begin to belch out smog, steam engines are built, the internal combustion engine is invented and eventually jumbo jets cruise through the atmosphere.
Where you can see alarming deviations though is if you take a small window along the graph, corresponding to a few decades. From the perspective of an individual human life span this seems like a long time, but in the scheme of things it's really not. On smaller scales random deviations begin to look significant, and you could perhaps persuade yourself that an exponential trend was beginning - rather like seeing faces in clouds or trying to find small features within noisy camera images. Also if you're selective about which data you choose then all kinds of theories are potentially supportable. So if I only look at the average minimum temperatures, or if I only look at the average temperature for November I might be able to persuade myself that some sort of anthropogenic foul play was going on.
So which camp would this put me in? Probably I'm a non-anthropogenic or maybe a slightly-anthropogenic warmer. Humans may have had some effect, but it's just not highly noticeable within the data. From this I'd predict that all the proposed carbon dioxide capture, footprint and trading schemes will have no noticeable impact upon the overall temperature trend. This still means that rising sea levels and changing weather patterns could be a significant problem though, and we should take whatever precautions are considered necessary to mitigate against these risks.
Approximate linearity
A line can be fitted fairly well to the average annual global temperatures. There's more variation in the past, but I expect that this can be explained due to less accurate thermometers and calibration methods. It may also be possible to fit a shallow curve.
The more imaginative you get, the more complicated lines or curves could be fitted to the graph, but usually according to the principle of Occam's razor the simplest explanation tends to be the best one. So with a bit of creativity we could maybe fit a nearly horizontal line to the left hand side, and a steeper slope to the right hand side. Or a shallow parabola or circular curve might be fitted. Or using a sliding windowed average the graph could be turned into a complicated looking series of oscillations.

In the interests of full disclosure, so that you can see that I havn't introduced my own fudge factors, the C# source code used to produce these graphs can be downloaded here. The program loads the data from a file called v2.mean and saves a few CSV files, which can then be visualized using the chart tool within OpenOffice spreadsheet.
