No, comments are not meant to be a first-class citizen, and up-voting a comment does not add reputation.
There are some badges related to comments, e.g.
But otherwise, no, up-voting a comment is more useful for other readers than it is for the person who wrote the comment:
When you up-vote a comment you're telling other readers that you agree with what the person said or felt it was a valuable contribution to the discussion.
This may encourage them to place more weight on the comment's value, and can often further encourage the post owner to make corrections if the comment was a critique or suggestion, since he/she can see that more than one person felt that way.
- As @sixlettervariables correctly points out, the most up-voted comments bubble to the top when there has been a lengthy discussion - this makes sure the most valuable comments are always visible even if some are hidden away due to noise.
Again, this is for the site in general, not for the commenter (whose comment was also for the site in general, not for self-benefit).
(Of course, the ego thing and reinforcement probably plays a bit there for some people, too - "hey, cool, someone agreed with what I said. I'm going to keep doing that." So I'm careful to not say there is no benefit for the commenter.)
Here on meta you may find the behavior to deviate a bit - often humorous or sarcastic comments are up-voted because they made the conversation funny or otherwise more enjoyable. This isn't usually the fashion on the main sites.