Gallup Analytics provides trends in public opinion polling, using a user-friendly web-interface. You can export tables, charts and plots, and maps for individual poll question responses. (You cannot access microdata through this portal.) This is a great choice if you only want to see trends and export graphs, and you do not need to do any statistical analysis.
Gallup Brain reports aggregate responses to individual questions asked in Gallup Polls going back to the 1930s. (To reach Gallup Brain, visit Gallup Analytics, and click on Gallup Brain on the bottom banner.) Use the keyword search to find questionnaires or browse by date. Use the “Locate a question” tool to discover similarly worded questions asked by Gallup over the years. You potentially could create trendlines going back further than Gallup Analytics with this feature.
Roper iPoll is a strong alternative to Gallup Brain. Search for questions by keyword. Microdata for more than 2,800 individual Gallup public opinion polls, from 1936 to mid-2015, may be available for download from the Roper Center for Public Opinion Research, Cornell University. This microdata includes the monthly-rotation Gallup Poll Social Series polls and also other Gallup polls.
Polling the Nations
Polling the Nations offers responses to surveys conducted in 100+ countries going back to the 1980s.