One way is to create a Blend and then Replace Spine.
Draw the object to be distributed. Copy it and move it a distance away from the original. Select both > Object > Blend > Make. Select Blend Options and enter a number in Specified Steps.
Draw the path you wish to distribute the objects on. Select the Blend and the path and go to Object > Blend > Replace Spine. This will probably distribute the objects along 3/4 of the path, therefore, you will need to use the Scissors Tool to cut the path at one of the anchors which will distribute them evenly across the whole path. Use Blend Options to increase or decrease the number of objects and thus the spacing.
Sounds like a lot but it is quite quick.
In Illustrator, Blend On A Path will yield evenly-spaced instances on a circle, but not on a non-circular ellipse. In AI, the distribution is affected by the curve handles. The closest feature to uniform distribution along a non-uniform path in Illustrator is a Scatter Brush, but that is problematic depending upon the specific artwork involved, because of the curve faceting behavior of Scatter Brushes.
Awkward workarounds can be devised using expanded dashes and a routine by which to replace the dashes with other objects. But there is no straightforward feature for uniformly distributing a Blend or Group along any given path in AI, as there is in other programs.
To follow up on the previous posts of creating a blend and replacing the spine, the uneven distribution may be turned into an even one by repeating Object>Path>Add Anchor Points until all objects fall into place. It may take some repettiton; you can see the gradual changes, and when nothing happens, you have done it once more than needed.
Thanks, this was very useful for me too!