Introduction
Transport demand can be measured either by final energy consumption (transport's energy demand) or in terms of km travelled. Final energy consumption is usually measured/estimated by statistical offices on an annual basis for a specified geographical / country scope. For km travelled, personal travel can be measured in passenger-km or vehicle-km the difference being the occupancy rate in passenger per vehicle. Freight transport demand is usually given in tonne-km.
Usually four modes are distinguished: Road, rail, shipping, air. Shipping is often further distinguished in maritime and inland waterway transport.
Time series can be approximated by e.g. measuring stations on roads. There are some data sets where hourly transport demands are surveyed on specific times in the year. In these surveys (e.g. Mobilität in Deutschland), usually further data on household, cars, driving purposes etc. is given.
Europe
Eurostat yearly energy consumption
http://ec.europa.eu/eurostat/web/energy/data/energy-balances
For years 1990, 1995, 2000, 2005, 2008-2014
Covers energy usage in EU, Balkans, Norway, Ukraine, Turkey, but NOT Switzerland.
Transport is divided into Road/Rail/Aviation/Navigation (boat?)/Pipeline transport/Non-specified.
EU Energy Trends to 2050 for yearly energy
http://ec.europa.eu/transport/media/publications/doc/trends-to-2050-update-2013.pdf
Contains predictions for total passenger-km and tonne-km for each EU country up to 2050, distinguished by public transport, car/motorcycle, rail, aviation, inland navigation.
Hourly vehicle count statistics for Germany
http://www.bast.de/DE/Verkehrstechnik/Fachthemen/v2-verkehrszaehlung/Stundenwerte.html
from the Federal Highway Research Institute (BASt)
Separate counts for different kinds of vehicles such as cars, trucks, buses, etc.