Portugal

Monthly data on underground use: https://www.ine.pt/xportal/xmain?xpid=INE&xpgid=ine_base_dados

INE publishes quarterly data on transport, latest available Q4/2019: https://www.ine.pt/xportal/xmain?xpgid=ine_tema&xpid=INE&tema_cod=1712

Republic of Moldova     

North Macedonia

Transport statistics, quarterly: http://www.stat.gov.mk/PrethodniSoopstenijaOblast_en.aspx?id=126&rbrObl=24      (click link to access table with more data in addition to bus statistics)

Romania            

Russian Federation        

San Marino       

Serbia  

Transport statistics, quarterly: https://www.stat.gov.rs/en-us/oblasti/saobracaj-i-telekomunikacije/prevoz-putnika-i-robe/

Slovakia             

Slovenia

Public scheduled road passenger transport, monthly: https://pxweb.stat.si/SiStatDb/pxweb/en/20_Ekonomsko/20_Ekonomsko__22_transport__02_22212_cestni_transport__02_22214_potniski_prevoz/?tablelist=true

Other transport statistics, monthly or quarterly: https://www.stat.si/StatWeb/en/Field/Index/22         

Spain

Passenger transport statistics, monthly: https://www.ine.es/dyngs/INEbase/en/operacion.htm?c=Estadistica_C&cid=1254736176906&menu=ultiDatos&idp=1254735576820

https://www.ine.es/jaxiT3/Tabla.htm?t=20239

Sweden

Railway transport, quarterly: https://www.trafa.se/en/rail-traffic/railway-transport/

Road safety statistics, monthly (SWE): https://www.transportstyrelsen.se/sv/vagtrafik/statistik/olycksstatistik/statistik-over-vagtrafikolyckor/

Bridge crossing data, monthly https://www.transportstyrelsen.se/sv/vagtrafik/statistik/infrastrukturavgift/

Switzerland 

New vehicle registrations, monthly https://www.bfs.admin.ch/bfs/en/home/statistics/catalogues-databases/data.assetdetail.12167618.html

Tajikistan           

Turkey 

Vehicle registrations, monthly https://biruni.tuik.gov.tr/medas/?kn=89&locale=en

Turkmenistan   

Ukraine

United Kingdom of Great Britain and Northern Ireland

Transport for London, Public transport journeys by type of transport (data for 28-day periods, last period ended 1Feb2020 as of 3rd April) : https://data.london.gov.uk/dataset/public-transport-journeys-type-transport

Highways England monthly summary data for all strategic roads (M and A; latest data currently February as of 3 April) ) http://tris.highwaysengland.co.uk/detail/monthlysummarydata

Vehicle registration monthly data (seem to have 6-month lag) https://www.gov.uk/government/statistics/vehicle-licensing-statistics-july-to-september-2019

Rail passenger data are quarterly (1Q2020 can be expected mid June) https://dataportal.orr.gov.uk/statistics/usage/passenger-rail-usage/

Quarterly bus statistics (1Q2020 can be expected end of June) https://www.gov.uk/government/statistics/quarterly-bus-statistics-october-to-december-2019

Shipping: weekly port visits https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronavirustheukeconomyandsocietyfasterindicators/dataasat2april2020#shipping-indicators

From a briefing: indicative road traffic and available public transport data, weekly https://www.gov.uk/government/publications/slides-to-accompany-coronavirus-press-conference-30-march-2020.

United States of America 

Border crossings US-Mexico, US-Canada, different modes, monthly: https://explore.dot.gov/views/BorderCrossingData/Monthly?:isGuestRedirectFromVizportal=y&:embed=y

Transportation services index, freight and passengers, monthly: https://www.transtats.bts.gov/OSEA/TSI/

National traffic volumes during the crisis (commercial data provider): https://inrix.com/blog/2020/03/covid19-us-traffic-volume-synopsis/

Railways, number of passengers transported, PKM, monthly: https://safetydata.fra.dot.gov/OfficeofSafety/publicsite/Query/rrstab.aspx

Amtrak monthly performance report (including passenger numbers, passenger miles, seat miles and train miles; latest February 2020 as of 6 April) https://www.amtrak.com/reports-documents

Road safety: New York Police Department (covering New York City): Daily traffic crash data, including injuries and fatalities https://data.cityofnewyork.us/Public-Safety/Motor-Vehicle-Collisions-Crashes/h9gi-nx95.

Uzbekistan

Other information:

Denmark    

Not direct statistics. Reported increase of 10% in speeding in big cities https://www.trm.dk/nyheder/2020/transportministeren-vi-skal-vise-samfundssind-ogsaa-i-trafikken/.

Ireland

Some estimates on impact on public transport from the National Transport Authority: https://www.nationaltransport.ie/news/covid-19-passenger-numbers-on-public-transport-services/

OECD-stat: data until Q3/2019

Info on navigation on the Rhine: https://www.ccr-zkr.org/13070000-en.html#02

Google mobility reports for countries show mobility at transit stations: https://www.google.com/covid19/mobility/