GE has and will pay large amounts of corporate income tax. GE paid no corporate income tax in 2010 due to a variety of special situations (including the 2008 meltdown of their finance business), and it was widely reported in the news. Since more normal tax years don't make the news, this has led many people like yourself to erroneously think some corporations don't pay income taxes.

Not necessarily true. Large companies can and do currently benefit from higher corporate tax and a complicated tax code. It creates barriers to entry for new companies competing in their market. If you make the tax code simpler it provides them less opportunities to specialize in avoiding taxes.