I've used Feedbin since before google reader shut down, which is a great service but requires a subscription. Very nice web app, super reliable, consistently gets new useful features. It handles email newsletters too, and stuff like YouTube and podcasts is handled well. For feeds that don't have full text it can go in and grab a reader view of the site, which rules. You can set up push notifications if you really need to.

$50/year is kinda high? But I use it every day and straight up never had any issues so I'll definitely stick with it.