Demographics:
New Jersey is the 11th most populated state with 8.8 million people in 2010 and a growth rate of 0.6% per year (28th). See New Jersey QuickFacts from the US Census Bureau
New Jersey is the most densely populated state with 1,189 inhabitants per square mile.
See the demographics page for more.

Science and Technology:
Edison (light bulb, 1879), Marconi (radio, 1899), David Sarnoff (RCA labs, invented TV), Bell Labs (Transistor, Big Bang proof, laser ...), Pharmaceutical headquarters for Merck, Schering-Plough, Aventis, Einstein spent a last part of his life (1933-1955) at Princeton's Institute for Advanced Study.

The Cultural Map which went viral on the web in December, 2011 divides the state into Cultural and Ethnic stereotypes.

I looked at the 2005, 2006 and 2009 CNN/Money Magazine's "Best Places to Live" lists. New Jersey, with 9, had the most cities in the top 25, followed by California (6) and WA, TX, MN, MA, & CO all with 5.

NJ ranked 6th in net migration out .

See demographics for more.

Income:
New Jersey has the second highest median household income in the country, behind Maryland.
New Jersey's income inequality index (Gini) was below the national index (good).
See Household Income for States: 2008 and 2009 at census.gov
NJ has three of the top 10 richest counties in the country | wikipedia
See demographics for more.

Politics:
NJ tends to vote democratic in presidential elections by a 7-15% margin. Since 1960 NJ has had 7 democratic governors and 5 republicans.

Other:
See North East New Jersey for more information on sights, recreation, etc.
US States Data: Population | Income | Best Places to Live | Crime | Health | Ethnicity
US City Data: Best Places to Live | Murder Rate
Interesting/Famous people