A very popular option today is to subscribe to your feeds using a website service. This allows you to check what's new at anytime, anywhere.
Feedbin is a straight-to-the-point feed reader with a clean three-column interface.
Configurable support for third party sharing services
Newsletter-to-feed conversion service
Full text retrieval for feeds that only give partial articles
$5 per month after free trial
Probably the most popular feed reader in the world, Feedly offers a in-depth array of features.
Discovery directory for finding more feeds on a topic
Inbuilt sharing and custom friend feeds. See what your friends are reading
Customisable interface, from compact lines to large visual galleries
$5.41 per month, billed annually. Free tier available
Inoreader bills itself as "The content reader for power users who want to save time." and its features and UI are designed around that.
Auto-tagging rules and automation
Discovery and sharing of interesting content
Limited ad-supported free tier, Starter tier $1.25 a month, Plus tier $2.50 a month
The Old Reader
Designed initially to accomodate users from Google's old reader service, The Old Reader focuses on the same quick reading and sharing functionality that Google Reader had.
Share and comment on friends' shared items
Premium subscriptions available for $3 per month
BazQux describest themselves to You Need Feeds:
"BazQux Reader focuses on your effectivity. It works fast, has clean interface, supports reading of Twitter/FB/G+/Instagram/VK, extracts full text from truncated feeds, shows post comments, has many view modes including mixed one, has search and filters and many more features. It has wonderful mobile website where you can zoom as well. And it's paid only reader so there are no ads or tracking and it updates your feeds in time."
$19 or $29 annually, or $149 for a lifetime subscription.