Media Matters for America is an organization dedicated to "comprehensively monitoring, analyzing, and correcting conservative misinformation in the U.S. media." They didn't, in my opinion, do a very good job in their recent piece on CEI and energy subsidies.
They write about Neil Cavuto recently hosting Chris Horner on a discussion over federal energy subsidies, and imply that CEI is supportive of subsidies to the fossil fuel industry, by noting that they fund us (and that Horner didn't discuss subsidies to the fossil fuel industry). CEI is, of course, against all energy subsidies. This doesn't mean that we get to discuss our opposition to them on television whenever we want.
They are correct that the fossil fuel industry receives more subsidies than renewable energy, but this doesn't really tell the full story. Energy subsidies should be evaluated on a per-unit basis. The fossil fuel industry is enormous, and many of the measured subsidies are just tax expenditures that grant various deductions and are large because of the size of the industry. Many of the "subsidies" they take advantage of are available to a large number of industries in the form of general exemptions in the tax code.
On a per unit basis, solar is crushing fossil fuel subsidies (and most other subsidies aside from biofuels). See page 18 of this PDF. Furthermore, the solar industry as we see it today isn't likely to exist without subsidies. There might be a small niche market but solar energy is still largely incapable of producing reliable electricity at rates that are even in the ballpark of cost competitiveness compared to coal or natural gas. The fossil fuel industry would still exist without subsidies.
Here is an interesting essay that suggests removing all energy subsidies might benefit the renewable energy industry.
Image credit: p373's flickr photostream.