Some interaction between the Sun's activity and the earth's climate is suspected and the level of contribution is hard to assign based on many other variables.
There are cycles in ocean currents, moisture and even CO2. And man made activity like dust in the air and aerosols have been shown to have some effect.
There was an extended period, 70 years, of solar inactivity in the 1600s called the Maunder minimum which seem to be correlated with extremely cold weather. The cause of that minimum is still unknown and the exact mechanism for how it would effect the earth's weather is not well understood. It would be foolish to assume there is no connection.
Solar "Weather" site Solarcycle 24
There have been 23 solar cycles monitored from Earth, with increased activity and then a quiet period. The reasons for these cycles is not understood. We may be at the end of a long and unexpected quiet period. Sunspots records go back to the year 1610, so some history and patterns can be analyzed.
Nasa in April 2009 on the deep minimum
and
Solar Wind Loses Power, Hits 50-year Low
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May 2009 Solar Cycle Prediction with some background on cycles
It adds up to one inescapable conclusion: "We're experiencing a very deep solar minimum," says solar physicist Dean Pesnell of NASA’s Goddard Space Flight Center in Greenbelt, Md.
"This is the quietest sun we've seen in almost a century," agrees forecaster David Hathaway of NASA’s Marshall Space Flight Center in Huntsville, Ala.
Fourm on past predictions of the lowest point of the minimum
Looking back into the archives, there are many many predictions of the start and size of solar cycle 24 given on the highest possible scientific authority that turned out to be flat out wrong.
