There were plenty of other aircraft flying too, including the superb Yak 3 (shown above) which was arguably the best fighter of World War II.
The Yak 3 (officially the Yakovlev Yak 3-M) was introduced by the Soviet Air Force near the end of World War II (1944) and 4,848 were produced in total. Its major advantage was good power to weight ratio which resulted from lightweight construction. It was relatively easy to handle and easy to maintain but did suffer from a few reliability problems including the engine and pneumatic system.
Sources: Wikipedia, Warbirds Over Wanaka 2010 Programme.
The de Havilland Vampire has been flown at most shows and is popular example of an early jet fighter, probably because it was produced in fairly large numbers and was used for so many years by various air forces. It was developed during the second half of World War II but wasn't ready for service until after the war ended (April 1945).
The unusual design incorporating twin booms for the tail meant the jet engine exhaust was kept short which prevented the power loss which had been a problem with engines running the full length of other aircraft.