If you have an account you need to export your feeds quick, fast and in a hurry. The instructions are on the front page of the Bloglines website.
I know that many people used Bloglines access multiple web locations no matter where they were or what machine that they were using. I certainly used Bloglines for class related sites and to track various types of information. It was very helpful.
Alternatives to Bloglines
If you have a Google account you can import your Bloglines feeds into Google Reader. This way you can continue to access and track websites from home, work or school.
My problem with using Google Reader is that I don't want all of my RSS feeds in the same place. I have entertainment links, educational and research links that shouldn't be intermingled.
Windows users might want to consider installing Feed Demon and Mac iPhone, iPad and desktop users may want to swing over to installing Net News Wire.
E-Mail RSS Readers:
Your e-mail program may have a News and Groups/RSS reader function. I use Thunderbird as my e-mail program and a supplemental RSS reader. Microsoft Outlook and other e-mail programs have similar functions.
The only problem is accessibility away from your primary computer.
Twitter and Facebook
Yes, this is an option if the website or blog faithfully announces new posts in their feeds. Not all do. And strange as it may seem not everyone has a Twitter or Facebook account.
You really should have some kind of link management or tracking system as long as it supports your online experience and your research needs.