Did sunspots sink the Titanic?
The Titanic sank on the evening of April 14th, 1912. The surface temperature of the seas was lower then and large icebergs were often seen floating in the Arctic and drifting southwards. The Titanic hit a very large iceberg and sank.
If you look at this plot you can see that there is a correlation between the surface temperature of the sea (SST) and the sunspot number. So, it seems that even if sunspots didn't leap out and hit the Titanic, they may have helped to sink it.
How does the radiation fron the Sun change?
The radiation from the Sun changes with solar activity. It increases when there are a lot of Sunspots. The increase in the visible is quite small, but the increase in the ultraviolet and X-ray radiation is much larger.
Here are some X-ray images of the Sun taken with the YOHKOH spacecraft. They go from solar minimum (no sunspots) on the right to solar maximum (lots of sunspots) on the left. Notice how dramatically the strength of X-rays from the Sun changes. We don't fully understand what effect the ultraviolet and X-ray radiation has on the Earth's climate.