Here is a first cut at ranking economic data. These lists are not exhaustive (I'm sure I left a few off), and the rankings are not static. As an example, right now initial weekly unemployment claims is ‘B List’ data, but when (if) the expansion takes hold, weekly claims will move unceremoniously to the 'D List'.

I've marked several indicators with '***' indicating I think this data is currently more important than usual. This includes weekly claims and several real estate related releases (delinquency reports, negative equity, vacancy rates).

For each indicator I've included a link to the source, and a link to the current graph gallery.

Some of the lower ranked data is useful as leading indicators. As an example, the Architecture Billings Index is a leading indicator for investment in commercial real estate. And the NMHC apartment survey leads changes in apartment rents and vacancy rates. Also some of the lower ranked data helps forecast some of the more important data.

A-List
• BLS: Employment Situation Report (Employment Graphs)
• BEA: GDP Report (quarterly) (GDP Graphs)

B-List
• Census: New Home Sales (New Home Graphs)
• Census: Housing Starts (Housing Graphs)
• ISM Manufacturing Index (ISM Graph)
• Census: Retail Sales (Retail Graphs)
• BEA: Personal Income and Outlays (graph)
• Fed: Industrial Production (graphs IP and Capacity Utilization)
• BLS: Core CPI (graph CPI)
• ***DOL: Weekly Initial Unemployment Claims (graph weekly claims)

C-List
• Philly Fed Index (Graph Philly Fed)
• NY Fed Empire State Manufacturing Index (Graph Empire Index)
• Chicago ISM: Chicago PMI
• Census: Durable Goods
• ISM Non-Manufacturing Index (Graphs)
• House Prices: Case-Shiller and CoreLogic (House Price Graphs)
• NAR: Existing Home Sales (Graphs Existing Home)
• NAHB: Housing Market Index (Graph NAHB HMI)
• ***MBA: Mortgage Delinquency Data (Quarterly) (Graph MBA delinquency)
• ***LPS: Mortgage Delinquency Data (Graphs LPS Delinquency)
• ***CoreLogic: Negative Equity Report (quarterly) (Graphs Negative Equity)
• ***AIA: Architecture Billings Index (Graph ABI)
• ***Reis: Office, Mall, Apartment Vacancy Rates (Quarterly) (Graphs REIS Vacancy Rate)
• ***NMHC Apartment Survey (Quarterly) (Graph NMHC Survey)

D-List
• Census: Trade Balance (Graph Trade Balance)
• Reuters / Univ. of Michigan Consumer Confidence Index (Graph Consumer Confidence)
• MBA: Mortgage Purchase Applications Index (Graph MBA Index)
• BLS: Job Openings and Labor Turnover Survey (Graph JOLTS)
• Census: Construction Spending (Graph Construction Spending)
• Census: Housing Vacancy Survey (Quarterly) (Graphs Homeownerhip, Vacancy Rates)
• Fed: Senior Loan Officer Survey (Quarterly)
• AAR: Rail Traffic (Graph Transportation)
• ATA: Trucking (Graph Transportation)
• Ceridian-UCLA: Diesel Fuel Index (Graph Transportation)
• NFIB: Small Business Survey (Graphs NFIB Survey)
• Fed: Flow of Funds (Quarterly) (Graph Mortgage Equity Withdrawal)
• STR: Hotel Occupancy (Graph Hotel Occupancy)
• CRE Prices: CoStar, Moody’s (Graph Moody's and CoStar)
• Manufacturers: Light Vehicle Sales (Graph Vehicle Sales)
• NRA: Restaurant Performance Index (Graph)
• Fed: Consumer Credit (Graph Consumer Credit)
• DOT: Vehicle Miles Driven (Graph Miles Driven)
• LA Port Traffic (Graph Port Traffic)
• BLS: Producer Price Index
• ADP Employment Report
• Conference Board Confidence Index
• NAR: Pending Home Sales

Sources (Government):
BEA: Bureau of Economic Analysis
BLS: Bureau of Labor Statistics
Census: Census Bureau
DOL: Dept of Labor
DOT: Dept. of Transportation
Fed: Federal Reserve

Sources (Industry):
AAR: Association of American Railroads
AIA: American Institute of Architects
ISM: Institute for Supply Management
LPS: Lender Processing Services
MBA: Mortgage Bankers Association
NAHB: National Association of Homebuilders
NAR: National Association of Realtors
NFIB: National Federation of Independent Business
NRA: National Restaurant Association
STR: Smith Travel Research