All the Twitter accounts I'd ever want to follow have fairly infrequent status updates so I just add them to my RSS reader and follow them that way instead of having to interact with Twitter's website or application in any way.
Twitter also removed direct RSS support for tweet feeds, and I did't like the hassle of having a third party in between.
It'd be really awesome if there was a tweet-ish open standard that anyone could implement, ala email or RSS (but supporting encrypted/password protected feeds). I feel like Google would be the perfect company to do it, but they decided they don't want to pander the nerds, and instead force G+ down our throats. (G+ I like. I just don't like how no one else is there)