If the rudder will move up and down in the shaft log as much as 1/4" or more, you need to check it out pretty quick. There are only two things (that I know of anyway) that will allow the rudder shaft to move up and down in the rudder log.
1) There is a good sized cotter pin that should be installed through a hole in the top of the rudder shaft just over the tiller arm. This is a failsafe device to keep the tiller arm from slipping completely of the rudder shaft if the pinch bolt mentioned elsewhere in this thread becomes loose. If the the tiller come off of the rudder, the rudder will drop out the bottom of the boat with the obvious consequences of no steering and a big hole (1 1/8") opening up in your boat.
2) There should be a thick (approx 1/4") nylon washer installed on the rudder shaft between the tiller arm and the rudder log. If it is not there, there would be vertical play in the shaft.
By the way, there are no replaceable bearings/ bushings in the rudder. If you have significant side to side play in the rudder, both the rudder shaft and log are worn. Frequent greasing will buy some time but both the rudder and log will need to be replaced as a unit. It is also possible to bore out the log to a larger diameter and machine a bushing to slip over the rudder shaft but this is somewhat involved.