Hi;
In a very real sense, of course it does -- because without the Sun, there would be absolutely no warmth on Earth besides what comes from plate tectonics, etc. But that is a slightly silly answer.

The Sun is not causing the global climate change (global warming) that we are now detecting -- at least not directly. The output from the Sun does vary, and that will cause numerous variations in some of the Earth's atmosphere (which I might add is very complex, and I'm not an atmospheric physicist so I don't want to say many specifics). But what we are seeing is a fairly steady rise in global atmospheric temperature over many decades, whereas during that time the Sun's output increased, and decreased, and increased, and decreased, etc. At the same time, we can measure the gasses in the atmosphere (Oxygen, Nitrogen, Carbon Dioxidee, Ozone, etc. etc) and we see that gasses which trap heat (e.g., Carbon Dioxide, Methane) are also increasing.

The Sun does play many roles in the really complex chemistry that occurs in our atmosphere, some of which may reduce global warming and some of which may make it worse. I do not understand atmospheric chemistry at all, but there are a lot of people doing a lot of research on it, especially here in Boulder, CO at the National Center for Atmospheric Research. Their website has a lot of good information. The bottom line is, however, that such chemical cycles which would follow the Solar cycles are now not following things in the same way they have in the past, because of the other input to the chemistry -- the increasing availability of those certain types of gasses for the chemical reactions to work with.

So -- the Sun does play many roles in the whole complicated system, but it is generally accepted that the Sun is not the cause of the increasing global temperatures.

Hi, as KD said, the output from the Sun does vary (according to the solar activity). The total amount of solar energy deposited on the Earth can also varies according to the Milankovitch orbital cycles. This orbital effect is responsible for long term climate changes (thousands of years period) associated to the Ice Ages and holocenes on the planet.

Evidences of the solar activity imprints on the terrestrial climate have been found in different natural archives, but such correlations alone are not sufficient to provide a final understanding on HOW that happen. One of the most famous evidence is related to the Little Ice Age, a cold period registered at the North Hemisphere during the solar activity minimum periods in the late XV century, early XVI. But defining the physical mechanism that links solar activity with climate changes is still a controversial subject.

Basically, the solar activity could affect the climate in 3 possible ways:

1) the variations of the total solar irradiance could direct impact the sea surface temperatures and hydrological cycle;
2) the changes of the solar ultraviolet flux changes the chemistry, temperature and composition of the upper and middle atmosphere. Due to the coupling between the atmospheric layers, those changes would induce changes near the surface.
3) the solar activity modulates the flux of Galactic Cosmic Rays (energetic particles that comes from outside of the solar system), and the interaction of those particles with our atmosphere would change the production of clouds (and that could cause a big impact on climate).

The open question is determine the significance of each solar forcing on the climate changes we observe.

My PhD student made an extensive analysis of the possible effects of rapid changes of the GCR flux on the near-ground temperature in different latitudes (she is defending her thesis next week and soon we will publish the cool resutls!). In conclusion, this is a very hot topic of study that integrates solar physicists and atmospheric scientists and there are still lots of work to do!