NASA offers a very convenient web-based tool to select and download the tiles you need; Reverb / ECHO. The tiles are in HDF format and use the Sinusoidal grid tiling system (proj4 definition:
+proj=sinu +lon_0=0 +x_0=0 +y_0=0 +a=6371007.181 +b=6371007.181 +units=m +no_defs). But you probably want to have the data in another data format and in another projection. NASA offers a very convenient cross-platform tool to reproject and convert the data (it also makes it very easy to mosaic tiles): the Modis Reprojection Tool (MRT).
But something I didn’t know is that it is also possible to open the tiles directly in QGIS. I tried before but I was never able to open the HDF files. I am not sure it was a problem with GDAL (used by QGIS to open all the different spatial data layers) or one of the underlying libraries*, but in any case, I just tried again, and it works now. And if it works in QGIS, it will (should) work with all your GIS programs that use GDAL, for example GRASS GIS.
Of course, opening the MODIS layers on top of other layers that use another project is not a problem in QGIS, just make sure to enable the “on the fly projection” option before opening the MODIS tiles. You can do this clicking the little icon in the lower right corner. Next, check ‘Enable ‘on the fly’ CRS transformation and select the projection you want to use (e.g., latlon WGS 84 – EPGS 4326).
Now all layers you open will be displayed in that projection (provided that the layers contain information about their projection).
* GDAL need to be compiled with HDF4 support (using
./configure --with-hdf4). I had already done that, but I recently installed the latest version of GDAL (version 1.9.2), so perhaps that solved the problem. On the other hand, I also updated Ubuntu to 12.10, so maybe some of the libraries GDAL depend on were updated.