Data for NOAA meteorological satellites can be downloaded through the NOAA CLASS archive.
Where, if anywhere, can I download data for the Chinese FY-3* meteorological satellites?
You can then download a "quickview" by clicking the little "picture" icon:
The full resolution data seemingly require payment.
---Information below is OBSOLETE. ---
Try FENGYUN Satellite Data Center. Getting the data from it can be a little tricky.
First click one of the icons:
In the next page, remember to select one of the "products" before clicking "next":
I haven't really used the system. It seems you need to pay for the data. However, "quickviews" are free:
I first searched the Chinese Government's Public Information site for
FY-3 and found 8 articles related to this kind of satellite, but no data sets. The articles had to do with beginning to use these satellites for various meteorological projects (November 2009) and the development of a system for processing this data (articles from 2009-2011). I did not see any actual data sets, however.
Try checking the UCS Satellite database. They track over 1000 satellites orbiting the earth.