How can I go forward and back frame by frame in media player classic? (left and right are jumping many seconds!)

The solution is to press

• Ctrl+← (left arrow) to jump by just one frame backwards,
• Ctrl+→ to jump forward.

I know the question was about Media Player Classic, but since it stopped development, thought it was worthwhile to point to Media Player Classic - Black Edition which is currently being developed. Just tried it, and it also supports Ctrl+← and Ctrl+→ to frame-step back and forwards.

Edit: There used to be an option to show frames in the playback time, but that appears to be gone. Now instead, if you right-click on the time in the lower-right, a context menu shows a checkbox to display milliseconds.

You need to turn on Turn fast seek off within the options menu.