Aggregators can live in two places: on your desktop or on the Web. There are some free desktop aggregators out there, but you'll probably have to pay a fee to get a more robust model. The list below is not exhaustive by any stretch of the imagination.
Windows Desktop Aggregators
Mac Desktop Aggregators
Web-based Aggregators
The services listed below are free. I recommend these as a good starting point if you're not sure what you're doing.
You may also see buttons like these when you're surfing the Web:
Rather than linking directly to a feed, such buttons enable a one-click way to subscribe to a feed via a Web-based aggregator service.