Users have the ability to upvote comments, as well as answers.
Upvotes for answers give an increase to reputation. Upvotes for comments give you nothing.
Can we give rep changes for comment votes?
Short answer: No :)
The reason for this is that we want to encourage people to actually answer the questions as answers rather than in comments. We also want to discourage people from having extended chats in comments, as that is not their purpose.
If there was rep earned for comment upvotes, then there would be less incentive for people to give answers. Also, to be fair it would require the ability to downvote a comment that someone disagreed with and take a corresponding hit to rep.
Lastly, remember that answers are incorporated into the knowledge base, are searchable and are able to give suggested answers to similar questions. Comments are not.
I agree with Jane S.
There is one other consideration.
On some questions/answers that stirred up controversy there were also complaints that moderators unfairly removed comments. They felt that comments from one side of the flame war were unfairly targeted by the moderators. They felt that their comments weren't chatty, but everybody else's were.
Now imagine the angst if points were attached to those comments.
Another perspective too is that comments are designed to be temporary by Stack Exchange. This link has a lot of detail about the purpose of comments (whether you like that purpose or not, this is a debated subject...).
The help center page on comments states:
What are comments?
Comments are temporary "Post-It" notes left on a question or answer. They can be up-voted (but not down-voted) and flagged, but do not generate reputation. There's no revision history, and when they are deleted they're gone for good.
Please note that you can always comment on your own posts, and any part of your questions. However, commenting on other people's posts is a privilege.
When should I comment?
You should submit a comment if you want to:
Request clarification from the author; Leave constructive criticism that guides the author in improving the post; Add relevant but minor or transient information to a post (e.g. a link to a related question, or an alert to the author that the question has been updated).
These reasons suggest that comments aren't really intended to provide lasting value to the site other than helping clarify/improve posts.