Orkin,
Your spindles are SHOT.
If you can physically MOVE the shaft, its WAY past being SHOT.
What brand/type mower is this on?
I've done a few spindle bearing replacements on JD's and SCAGS. All with the use of a press. Without a press, I wouldn't suggest that YOU tackle this.
Plus, with mail order companies offering COMPLETE spindle assemblies, replacing bearings is just not worth it.
You can get complete spindle assemblies for $50. Just R/R and your set.
You can spend upwards of $20 on just bearings and other clips and keys, etc. Then whats YOUR time worth, or YOUR dealers time worth?
Just buy the complete assembly.
Then if its a SCAG or a through bolted spindle, the inside diameter of the spindle shaft can become enlarged allowing the spindle bolt to "float" in the spindle. Just replacing bearings will NOT fix this. Plus, many times the reason for the bearing failure is a BENT spindle shaft. Sometimes not even VISIBLY bent.
Hope this helps.