@Fomite's answer is spot on. I would like to expand further on the differences between a biased review, a lazy review, a significantly erroneous review, and a negative review, and which do/don't warrant an appeal.
The examples given in this post come from a contest held by the always-excellent FemaleScienceProfessor. Quite a few are real reviews, or based on real reviews.
Does warrant an appeal, if it's the reason your paper was rejected. Often editors are smart enough to identify a biased review on their own, and will simply discount its advice.
Example #1 (here, the reviewer clearly lets his personal goals get in the way of a fair review):
I am afraid I cannot support the publication of this paper. The authors present an idea that I myself have had for some time and just haven’t gotten around to writing it up yet. I think that when I write my paper, it will be better than this one. These authors would be well advised to wait until my paper is published, and then they can cite it.
Since the author is a woman, I had lowered my expectations accordingly, but the author did not even meet those. Even though I have never done experiments in my life and have never used any of these techniques, the experimental results presented were completely misinterpreted in my distinguished opinion.
Does not warrant an appeal. If all of your reviewers give you a lazy review, you need to do a better job exciting the reader (thereby motivating the reviewer to carefully read the whole paper in detail because it's such compelling reading.) (Very rarely, this can be an indication of a bad journal/conference and you should find a better place to submit your work).
The topic of this paper is not of critical importance to furthering knowledge.
Sent from my iPhone
Paper Title: Linear and Nonlinear Methods to solve XXX
Review: "Why is the approach limited to linear methods, and the author does not propose nonlinear methods?"
Significantly Erroneous Review
(per JeffE's suggestion)
This is a distinct case from the Lazy Review. It does not include the case where the reviewer "erroneously" concludes that your work is not interesting or useful, just because you disagree with this conclusion. It does not include the case where the reviewer says "I am concerned about X" and you believe you've adequately addressed X.
It does include cases where a review is affected by a significant factual, logical, or mathematical error. This is grounds for appeal.
Example (the reviewer is mistaken as to the meaning of "graph" here):
Paper title: Graph analysis of System ABC shows differences in A-B connections during Condition X vs. Y
Review: This paper uses a novel method to study ABC system dynamics. However, I don't know anything about graph analysis so I'm going to interpret the paper through the lens of a different analysis method I do know something about. Thus the only constructive feedback I can give is that this paper is a poorly written explanation of a structural equation model of XYZ - the conclusions drawn make little sense given the data, i.e. they frequently refer to "graphs" but all I see are these pictures of circles and arrows.
(A minor error is highly unlikely to be the reason for a rejection. Therefore, for a minor error, an appeal is not likely to be successful - an appeal will be useful only if the point of appeal was the reason for the rejection. In the case of a minor error, I would advise to use the reviewer's mistake as an opportunity: to clarify in the text points that might lead people to mistakenly discount your results, or even to decide to ignore the criticism because it's not a common enough misconception to be worth addressing in the paper.)
A review that does not fit into the above categories, but still criticizes your paper, is just a negative review. It is not grounds for an appeal. It should be taken as constructive criticism, and you can use it to make your paper better.