Research Funding distribution across discliplines
In the UK, the EPSRC (Engineering &amp; Physical Sciences Research Council) has a handy visualisation on their website to see the current funding distribution within their remit.

A similar visualisation has been created for the BBSRC (Biotechnology and Biological Sciences Research Council) - also UK. Although this only appears to be for projects active in 2012.

UberResearch compiles data on research funding, however, their service is not freely available. They do have some samples, which my be interesting. They appear to have data from the UK, US and EU. I've never used this service so cannot comment on its usefulness.

Most of the public funding bodies provide data on funded projects on their websites. However, it would require a lot of processing to make visualisations of it.