You can find plenty of summary data, but I have not seen any publicly available raw counter data. Here's some summaries:
Federal Highway Administration
Traffic Volume Trends is a monthly report based on hourly traffic count data reported by the States. These data are collected at approximately 4,000 continuous traffic counting locations nationwide and are used to estimate the percent change in traffic for the current month compared with the same month in the previous year.
Arizona Dept of Transportation
The annualized average 24-hour volume of vehicles at a given point or section of highway is called a traffic count. It is normally calculated by determining the volume of vehicles during a given period and dividing that number by the number of days in that period.
California Dept. of Transportation
The Traffic Data Branch is responsible for the collection and dissemination of historical volumes (counts). We also produce the Mobility Performance Reports.
TRAFFIC COUNTS, also called Traffic Volumes, are available in various formats, and are only for the State Highway System. Highways are signed as Interstate, California State Route, or United States Route.
Colorado Dept. of Transportation
This is the access point to information frequently used for transportation planning and project development. Information is provided on current and projected traffic volumes, state highway attributes, summary roadway statistics, demographics and geographic data.
Florida Dept of Transportation
Welcome to the Florida Department of Transportation's Traffic Information site. This site provides statistical traffic information for Florida's State Highway System.
Indiana Dept of Transportation
INDOT Interactive Traffic Count Map showing the annual average daily traffic (AADT).
Maine Dept of Transportation
Traffic Monitoring is responsible for the collection of all types of traffic data including traffic volumes, vehicle classification, turning movements and special studies as requested by the Department. The reporting of traffic volumes is accomplished through two distinct methods involving the Continuous Count and Coverage (i.e. short term) Count programs.
Massachusetts Dept of Transportation
The Massachusetts Highway Department conducts an annual traffic data collection program. This data is available online by autoroute and city/town list or as an interactive map. You can view data for a specific town from the Town Index, for numbered routes from the Numbered Route Index, or you can use the interactive map to browse data by area. You can also download the complete spreadsheets
Michigan Dept of Transportation
2012 Average Daily Traffic (ADT) Maps
Minnesota Dept of Transportation
Thousands of traffic counts are collected on Minnesota roadways each year. This information is used to produce volume, classification, speed and weight data as well as traffic forecasts, reports, maps and analysis.
New York State Dept of Transportation
The Highway Data Services Bureau is responsible for the collection and dissemination of information on the extent, use and condition of the public roadway system in the State of New York. The Bureau consists of three sections: Highway Data, Traffic Monitoring, and Pavement Data.
North Carolina Dept of Transportation
Annual Average Daily Traffic (AADT) Traffic Volume Map presents the traffic average for the year at specific points on North Carolina highways. Data is collected at more than 40,000 locations throughout North Carolina using Portable Traffic Count Stations. AADT map is typically published at the later part of the summer.
Ohio Dept of Transportation
Traffic Count Information & Maps includes Traffic Survey Reports and Traffic Survey Flow Maps. The Traffic Survey Reports list an estimate of Annual Average Daily Traffic (AADT) volumes separated by cars (Pass &A Com’l) and trucks (B&C Com’l) for all Ohio Interstate, US and State highway system routes.
Oregon Dept of Transportation
The Transportation Systems Monitoring (TSM) Unit has the mission to formulate a system to collect and process traffic related data on Oregon´s Highways. TSM provides traffic volumes, flow maps, trends, manual counts and vehicle class on state highways to Federal, State, Local, private and public constituents.
South Caroline Dept. of Transportation
The Traffic Polling and Analysis System provides traffic data and graphs from traffic counting devices on South Carolina's Highways. This system is intended for the general public to view current and historical traffic information during hurricane evacuation events
Tennessee Dept of Transportation
An AADT traffic volume is used throughout the project planning process to provide projected volumes of traffic. It is based on a 24 hour, two directional count at a given location. This raw traffic volume is then mathematically adjusted for vehicle type, determined by an axle correction factor. Then this volume is statistically corrected by a seasonal variation factor that considers time of the year and day of the week.
Washington State Dept of Transportation
The Annual Traffic Report (ATR) summarizes traffic data maintained by the Washington State Department of Transportation for the State Highway System. The report includes Annual Average Daily Traffic (AADT) figures and truck percentages, when available, for locations where data collection has occurred within the past four years.
Wisconsin Dept of Transportation
Wisconsin Department of Transportation (WisDOT) traffic counts are now part of an interactive map that allows you to view counts anywhere in the state.
Chicago, IL Transportation
Average Daily Traffic (ADT) counts are analogous to a census count of vehicles on city streets.
Arlington, VA Transportation
Arlington County Regular Traffic Count Data is available in Portable Document Format (PDF).
Delaware Valley, PA Delaware Valley Regional Planning Commission
British Columbia, Canada Ministry of Transportation
The Ministry of Transportation and Infrastructure's Traffic Data Program monitors traffic volumes at several locations throughout the province. This information is used by ministry staff to help support planning, design, construction, and operation of the Ministry road network.
United Kingdom (UK) Dept of Transportation
Traffic counts provides street-level traffic data for every junction-to-junction link on the 'A' road and motorway network in Great Britain.
New South Wales, Australia Roads and Maritime
Traffic Volume Data books, sorted by Roads and Maritime Services regions, containing the Annual Average Daily Traffic (AADT) volumes for various roads.