As with the vocabularies, the gene product sets from contributing groups are freely available; you can download them from the annotation downloads section of the GO website. Those files contain all evidence pertinent to the annotation, including database IDs and gene product names, as well as citation and evidence data. The format of these tab-delimited files is described in the GO annotation file formats guide.
Currently, we support up to 10,000 download items at a time using AmiGO, but we are working on expanding that number. When results require a download of more than 10,000 items, it is more appropriate to use GO's SQL environment (remote and locally):
Alternatively, depending on the exact nature of your query, you may consider using command line functionality on the raw data files, available from the Download Annotations page.