If you are looking for a dataset going back a bit further, but still sticking to satellite and radar data, GPCP (Global Precipitation Climatology Project) goes back to 1979. The limitation of certain TRMM datasets, in addition to the relatively short length of the project, is that they only cover the tropics and so you lack data in the mid-latitudes and higher for a proper global analysis. Some TRMM datasets extend up to 60 degrees latitude by incorporating radar and other sources into the final product.
If you want to go back even further (to 1901 globally) the GPCC (Global Precipitation Climatology Centre) is a good place to start. Anything before the launch of TRMM in 1997 will likely be a collation of various data sets, so the comparability between regions is occasionally questionable, although there are robust ways of correcting for this applied to the datasets. This is a truly global data set, according to their spatial coverage description (90.0N - 90.0S, 0.0E - 360.0E)
Beyond that, the datasets are patchy between different countries. You would have to collate your own global dataset from the various national meteorological archives. The UK precipitation archives (Armagh Observatory), for example, go back to about 1795, but I'm not aware of them being included in many (any?) global collations.
N.B. Almost all of this data will be in some form of Cartesian or geographic co-ordinate format, so you probably won't be able to look up individual places or countries, but will need to extract latitude and longitude bounded regions from the data.
Link to the GPCC download site:
GPCC gridded data download