I noticed to my surprise today that the very early Soviet flights were to a very high inclination - all the Vostok flights were between 64.9° and 65°, and the Voskhod flights were at 64.7° and 64.8°.
After this, Soyuz 1 was at 50.8°, and subsequent flights seem to have been at or around a standard 51.6°. The only exception appears to be Soyuz 22, which went to 64.75°. On the American side, all orbital Mercury flights were at 32.5°; early Gemini flights were the same before dropping to 28.8°. Apollo lunar flights used a parking orbit around 32.5°, and Skylab was at 50°. Several Shuttle flights went to 57°, and STS-36 made a rather complex flight to 62°. Vandenberg launches would have gone to nearly 90°, but they were cancelled.
Generally speaking, the high-inclination flights seem to have been aiming for earth observation opportunities (or in the case of STS-36, to deploy an earth observation satellite). Wikipedia explicitly mentions this reason for Soyuz 22.
However, it's not clear why it was used for the earliest Vostok/Voskhod flights - was it to support earth observation objectives? Was there a political justification, to ensure it could be observed as widely as possible? Was it a quirk of the launch system which made this inclination easy to achieve?