There are currently 47.5k questions with close votes.
This seems to be quite a problem in my opinion and I think the close vote policy needs to be reviewed.
A few suggestions:
Higher reputation users get more votes (apparently already happens)
Votes of higher reputation users are more significant (e.g. 2x or 3x)
Higher reputation users are allowed multiple votes per question
Very similar to more significant votes, except that casting additional votes has a cost.
Related to this (+48). My comment there suggests a safer option - 50k = 2 votes, 100k = 3 votes and no question can have more than 2 additional votes (i.e. max 2 users each 2 votes ((2-1)*2=2) or 1 user 3 votes (3-1=2)) (thus absolutely no question can be closed with less than 3 users (except maybe with mods))
Any of the above 3 suggestions, but rather than using high rep as judging factor, using reviewing ability (how to judge this?)
Increase reputation required to vote to close own questions (not sure how many of the questions this is or how much reputation is required)
Voting affects reputation (for motivation) (sounds like a good idea for all types of review - it would stop reviewers that approve inappropriate posts)
Increase if people agree, smaller decrease if they don't, though this isn't currently applicable to close votes, though maybe it should be.
A negative voting reputation doesn't decrease your overall reputation, but significantly reduces the number of votes you're allowed (or simply disallows voting)
Once-off flush. The number of questions appears to be pretty stable (from checking over the past few days / weeks), so a once-off flush may fix the problem.
The reasoning is that it being that high looks bad (does it matter? I don't know) and may be demotivating to potential reviewers.
Remove all the questions with closed votes from the queue and trickle-feed them back into the system, preventing the queue from building.
Similar to the once-off flush, but doesn't into-the-void-ify votes. The reason to do this is probably more psychological than anything else, and possibly that tending to newer (presumably more significant) requests could get delayed (this doesn't seem to be such a big problem).
Decrease the number of views required for votes to start expiring. Presumably most of these are those with less than 100 views (otherwise they would expire), so just decreasing this limit may work.
Have the Community user poke questions with close votes more often than other questions
This will get the question more attention to get up to 100 views (so votes start expiring) or for it to get more close votes to be closed.
Lower reputation required for close vote privilege (this is a terrible idea, just included for completeness)
Order by date / number of votes already cast on question
Not so much a suggestion as a consideration. I don't know how questions are currently sorted, but one of the above or a combination of the 2 might be a good idea.
Better interface for the review queue
I find the current way of reviewing close votes unworkable for various reasons. I'm thinking a nice interface very similar to how you can currently browse questions.
Decrease number of votes required to close a question
An irritating little note popping up somewhere occasionally for 3k+ (4k+? 5k+?) rep users reminding them to use close votes if they don't already
UPDATE - 2013/04/04:
Rather significant edit.
I've seen a steady increase over the past 2 months. Sitting at 51k now. I think it's safe to say something needs to be done.
Data explorer queries:
Get open questions with close votes, sorted by most votes including a clickable link to question - useful for reviewing if you find the review queue unworkable (no badge for you, unfortunately).
Get count of open questions per number of close votes (maybe a little off).