The last decade has seen a revival of various hypotheses claiming a strong correlation between solar activity and a number of terrestrial climate parameters. Links have been made between cosmic rays and cloud cover, first total cloud cover and then only low clouds, and between solar cycle lengths and northern hemisphere land temperatures. These hypotheses play an important role in the scientific debate as well as in the public debate about the possibility or reality of a man-made global climate change. Analysis of a number of published graphs that have played a major role in these debates and that have been claimed to support solar hypotheses shows that the apparent strong correlations displayed on these graphs have been obtained by incorrect handling of the physical data. The graphs are still widely referred to in the literature, and their misleading character has not yet been generally recognized. Readers are cautioned against drawing any conclusions, based upon these graphs, concerning the possible wisdom or futility of reducing the emissions of man-made greenhouse gases.