Is it appropriate to up vote a question when it is neither appealing nor interesting to me, but has unnecessary down votes?
In other words, is it appropriate to up vote a question just for the purpose of removing down votes?
It depends; do you think it appropriate to silence others' opinions? That is effectively what the activity you propose is.
A downvote expresses someone's opinion on a post; e.g. maybe they think a question doesn't show any research effort, is unclear, or is simply not useful.
Voting for the sole purpose of removing a downvote is quite directly acting to remove someone else's ability to voice their opinion. If you believe suppressing such opinions is appropriate... then I suppose upvoting to remove such a downvote would be appropriate. Otherwise, it's not appropriate.
(aside: there is a difference between "I upvoted to remove someone's opinion" and "I upvoted because I think this is a good question, although I wouldn't have paid enough attention to form that opinion if it wasn't downvoted")
In general I do not consider it as appropriate to cast votes only to balance other votes. However, I am of the opinion that it is reasonable to take the current score of the question into account when voting (not doing so makes the score depend a lot on visibility, which is not optimal in my opinion).
I am less likely to up-vote a post that is already at score +3 than I am to up-vote the same post at score 0 or score -1.
Put differently, I think it can be alright to be more generous with ones up-votes on posts that currently have a poor score. However, there should at least be some reason intrinsic to the post for the vote, too; just going around the site and balancing down-votes one does not understand or like is not a good thing to do though.
In summary: No.
For, when a question is "neither appealing nor interesting", you'd best move on to some question you do like. Chances are you can contribute more to the community there. If the downvotes mystify you, you can always leave a comment stating something like "I don't understand the downvotes to this question." You might be missing something, or otherwise trigger an explanation of the downvoters, which in turn can help OP in improving their post.
In a more general situation, upvote based on the post. If you suspect the downvotes are caused by something missing from the post you can:
The bottom line is, in my opinion, that if you dislike the symptom (the downvote), then you'd better invest in eliminating (or at least, identifying) the cause (the quality/clarity/... of the post) rather than just combating the symptom.
Your own upvotes are a disjoint consideration from the above. Although I might add that if you see an opportunity for an edit that would make the question upvote-worthy to you, by all means, edit it.
If a question is in danger of being deleted due to a negative score, and if deletion of the question would result in deletion of an answer which you feel should remain on the site, then, yes, by all means, upvote the question.
Yes, it is perfectly appropriate to upvote a question in order to cancel a downvote.
The only function of votes is to provide information on the quality of the question.
Downvoting is a judgment on that quality and if one considers that a downvote is undeserved it is quite reasonable to correct this misinformation.