I use a desktop app, QuiteRSS. I'm in front of the same computer all day so I don't need a reader that's synced across devices. Whatever you use, I suggest you look into subscribing to everything you can using RSS (HN, Reddit, YouTube), it's a much better experience than rescanning sites over and over.
I've started using email where possible. As long as they only send me new articles I'm happy. The second they spam me, I don't read them anymore. Unfortunately not everywhere offers it.
I loved Google Reader. When it died, I tried several replacements. Feedly was the one I ended up using. I'm not as fond of it as I was of Reader, but in my opinion it's the best of the ones I tried.
I've recently been looking to use web based tools where possible and tried out feedbin. If it stops running I can self host as it's open source. In the meantime I'm more than happy to pay the monthly sub for something I use daily.
I wrote a personal bookmark web app to keep track of sites I visit frequently, group them, tag them, and search. It was a fun project, and I'm the only user, so there isn't any support overhead. It runs on a $5/month Linode instance.
Since I often don't have a connection Pocket is my goto for reading (though it's awful at math). https://feedhuddler.com automatically populates Pocket from rss.
