The numbers in the wikipedia table you link to are suspect in my mind. The source article doesn't provide the data that the wiki article suggest. If we believe the data that are in that article, private industry in the US spends $280 billion on R&D while the government spends $126 billion. While the private industry funding is staggeringly large, it probably means that no individual company is spending huge amounts and therefore can probably be left out of your ranking.
Of the $126 billion that the US spends, the DOD and NIH spend $64 billion and $26 billion respectively on research which is 70% of the pot. Additionally, NASA, NSF, FDA, and DARPA have budgets of $18, $7, $4, and $2.8 billion, respectively. While that is not all R&D, it probably covers the big players.
As for other countries, the RCUK, which is the major funder in the UK has a total budget of £3 billion which is spread over the 7 sub councils. In Germany, the DFG and MPI have budgets of €2.7 and €1.5 billion.
If we ignore Japan and China (and I have no idea who funds research in those countries), the list looks like
- US DOD: $64 billion
- US NIH: $26 billion
- US NASA: $18 billion (maybe if they actually do R&D)
- US NFS: $7 billion
- everybody else: