According to Official Guinness Records,
The most relay teams to complete a marathon is 2,373 achieved during Vienna City Marathon 2010 in Vienna, Austria, on 18 April 2010. Each team had 4 members, running lenghts of 16.1 km (10 mi), 5.7 km (3.54 mi), 9.1 km (5.65 mi) and 11.295 km (7.02 mi). The marathon was 42.195 km (26.22 mi) long.
For a complete list of 2010 records, please visit 2010 Guinness Records in Austria.