Tsunamis, nuclear explosions, epidemics, certain keywords received on the police scanner, public transit delays or cancellations, good deals on Ebay for HP 41CX calculators.
I would like to know about things that the powers that be specifically don't want me to know about. Laws that are being slipped through under the cover of night. Any changes to civil or human rights issues. Funding connections to politicians. Abuses of power.<p>Basically, a transparency module. And yes, I know this is what newspapers used to do, and some blogs attempt to. The signal to noise just isn't great and delivery is not very directed.
Interesting question. Are there certain constraints or parameters to your question? If not, here are some things that comes to my mind:<p>1. Sudden (unexpected) weather changes
2. Location-relevant deals/coupons (relevant to my interests)
3. Any breaking news (in a similar manner to how things tend to break on Twitter b4 mainstream news broadcasts it)
4. If friends/family are within a local proximity
From what's not readily available -- earthquakes in the area, tsunamis, power/phone/cable outages and fire alarms at specific locations (think - a street block), Amber alerts, public service announcements.