Plotting temperature history for the
G8 nations using the Global Historical Climatology Network data we get the following.

There's a spread of warming and cooling trends, and if we then take the average of all these graphs the result looks like this.

At first this seems exciting, because it appears to show some increase in temperature in the late 19th century, which could indicate an anthropogenic origin. However, comparing with the first graph we can see that the low temperatures up to 1870 are the result of missing data for Japan. Missing data, if there's enough of it, can produce phantom increases or decreases in the global average trend.
To get more reliable averages more data is needed, so I expanded the scope to the
G20 nations. I'm picking the G8 and G20 because these are highly industrialized nations which could be expected to be producing large quantities of atmospheric pollution.

Then calculating the average.

Again the initial low temperatures are not due to anything dramatic or sinister, but are simply an artifact of missing data. You can also see that the downward blip around 1993 is the result of missing data which makes the average value slightly smaller. But overall this gives a very convincing linear warming trend, indicating a rise of about two degrees per century.
So at this point I'm sitting smugly thinking to myself that I've identified the signal behind the noise. But wait - could this two degree slope be purely an artifact of missing data? We already know from the pre-1870 period, and the 1993 blip that missing data plays havoc with the averages. To investigate this possibility I removed three nations from the list which do not have a very complete temperature record over this period - Korea, Turkey and Saudi Arabia (sorry guys), then re-plotted the graphs. The resulting plots look cleaner than before.

When we again take an average of these, something unexpected occurs.

The nice slope, which fitted to a line so satisfyingly, almost completely disappears. Removing pre-1880 temperatures the graph looks like this.

Bear in mind that these are the majority of the world's most industrialized nations, including the Russia, China, USA and the manufacturing giants of Europe. They should be producing an increasing volume of atmospheric pollution over this time period.
Conjecture: could the global average temperature slope be the result of significant missing temperature data, with the relatively recent introduction of temperatures for countries closer to the equator (eg. within Africa) producing what appears to be a warming trend?
To find out I extracted temperature histories from the entire data set which were more than 98% complete. This means that for these countries there has been an almost unbroken series of temperature measurements, so apparent structure in the resulting overall average can't be ascribed to missing data.
30 countries fit this criteria. This is a larger number than the G20, so the overall average should be more reliable.

From this the two degree per century linear slope once again emerges triumphant.

Even if this hasn't convinced anyone else, I've managed to satisfy myself using the raw data that global warming is occurring, that it's following a linear trend which likely precedes the industrial revolution, and that the temperature graphs typically shown in the media and on the Met Office web site are significantly distorted by continuity gaps in the temperature data such that what appear to be sudden jumps or dips are actually just phantoms.
Another thing which has become apparent from these experiments is that selectively adding or removing temperature series can alter the slope of the overall average temperature graph, so by inclusion, omission or perhaps attempted interpolation a variety of climate theories could be supported. For example, if I included temperatures for Canada, Russia and China in the above graph, which are all following a cooling trend, this would tend to pull the slope down towards a flatter profile. This should be borne in mind when assessing the likelihood of climate change predictions.