Al Jazeera
The best source of news. Funded by the moderate Qatar emirate. They take a critical view of dictatorship and are letting the protesters speak their mind. NOTE: they are sometimes biased the wrong way. For instance, in the case of Bahrain they are not giving the protest movement fair coverage (especially true of their Arabic coverage).
Al Jazeera has live country blogs for hot spots. For instance, their current
Feb 22 blog on Libya
NY Times - Middle East
Associated Press Wire
The Guardian - progressive UK newspaper.
CNN
Crowd Voices - tracking voices of protest.
How to Use Twitter
You can search Twitter to get a flood of short messages and links to stories. Typically the stories are anywhere from several minutes to a couple hours old. Generally I like to search for a country name. For Jordan, the name is too commonly used for people, so I like to search for "Jordan Protest". It is also useful to search for protest related tags like #jan25, #tahrir, or the city name (Tripoli, Benghazi) or the leader's name (less useful if there are multiple spellings - like in the case of Ghadaffi).
I like to skim read and hit refresh a lot to get new stories. You'll see a lot of repeats.
My twitter: @online_activist
It pays to find people who are first-hand sources. Often if you follow the trail of retweets you can find the original source and just follow them directly.