user20: People might want to ask about anime / manga which are similar in style / story to the one they just watched or liked. Should they be closed as "not constructive", since they are by-nature were preference-based and you can't objectively say which anime is truly similar to which other one? There are also sites like MyAnimeList which provide recommendations of similar series on series' page.

user69: No, I do not think these should be allowed.
Over on Arqade, we allowed game recommendations for quite a while, but they were ultimately disallowed because of the inherent problems that make them unsuited for the SE engine.
Subjectivity Problems
The subjectivity of criteria for recommendations is the first problem, which you mentioned, as that very easily skews answers to becoming Not Constructive. When someone asks for a recommendation based on their enjoyment level of an existing work, it is practically impossible to give a canonical answer because of enjoyment level being so subjective from person to person.
If someone really enjoyed Serial Experiments Lain and wants something similar based on X, Y, and Z subjective criteria, how are we to determine what an appropriate, canonical answer is? Even if you look at objective criteria (cyberpunkish aspects, scifi setting, etc.), the determination of a canonical answer is still difficult because the asker may not feel that certain characteristics of another series match up "enough" to their criteria.
Can't we allow them if they're specific enough?
Again, determining the criteria for "specific enough" is incredibly difficult. If one person asks for 5 specific characteristics and another only asks for 4, do we close the one with 4? How vague or specific should said criteria be? This creates confusion for both drive-by visitors and for the community as a whole.
Inaccurate Voting Problems
This is a huge issue with recommendation-style questions. Specifically, inaccurate voting issues are when answers end up garnering upvotes based on popularity/enjoyment/other subjective criteria instead of answer quality. This is bad.
For example, when we still allowed these on Arqade, any game-rec question that had an answer with "Portal" in it garnered a large amount of upvotes simply because Portal was mentioned in the answer. These questions turned into impromptu polls that awarded reputation that was not based on quality content, which is ultimately what we want to reward.
List Maintenance
While a bit minor in comparison to the above 2 problems, the issue of maintenance when allowing these questions does play into the problems they have. When asking for a series recommendation, any new entries that fit into the (subjective) criteria the asker wants would have to be updated. This creates a maintenance problem the community has to deal with, keeping possible answers up to date in order for the question/answers to remain relevant. Again, this can be a somewhat minor issue, but it can still be a problem, especially considering the propensity for these questions to be asked in high volume.
So what do we do?
Using the associated chat room is a good solution for areas of interest to the anime/manga community that can't be dealt with/aren't appropriate for the site proper. While some suggest a separate recommendation room, based on experiments with a separate game recommendation room in the past, I would suggest directing people to the main anime/manga discussion room, as it will likely have the most activity. Making people go to a recommendation specific room may not be fruitful at all, as it depends on the number of people willing to hang out there and only talk about recommendations. We've found on Arqade that directing them to our main chat room has netted the best results.
In addition, once the site picks up in traffic, we may be offered an Anime blog sometime in the future, which is also a good place to list more permanent resources for subjects like this. You could even do a recommendation-a-week blog or something like that!

user-1: Absolutely not.
I've been a longtime lurker on the Stack Exchange sites (notably, SciFi) and I can say that these types of questions are always not constructive. 
The Not Constructive "off-topic" close reason has the following text appended to it:

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or specific expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, see the FAQ for guidance.

Questions that ask for anime recommendations are:

Not empirically answerable. -- They don't have one, or even finite, correct answers.
They're flamewar bait. -- People will get into comment-fights about which anime is better, which is the better recommendation, why someone's rec was wrong, etc. I don't want to see that kind of drama here.
They're usually polls. -- A non-terminating list of answers that get votes by popularity? Classic poll. Plus, mainstream titles (Naruto, Bleach, One Piece) are going to get more attention than less mainstream / niche shoujo or seinen/josei titles (Sainkoku Monogatari). 
They're an excuse for discussion. -- Good recommendations will require extensive knowledge about the OP's tastes and likes/dislikes. This is better done in chat.

Basically: always close these questions as Not Constructive "off-topic" and hold these discussions in chat instead.

20: <p>People might want to ask about anime / manga which are similar in style / story to the one they just watched or liked. Should they be closed as "not constructive", since they are by-nature were preference-based and you can't objectively say which anime is truly similar to which other one? There are also sites like <a href="http://myanimelist.net" rel="nofollow">MyAnimeList</a> which provide recommendations of similar series on series' page.</p>
 69: <p>No, I do not think these should be allowed.</p>
<p>Over on <a href="https://gaming.stackexchange.com/">Arqade</a>, we allowed game recommendations for quite a while, but they were <a href="https://gaming.meta.stackexchange.com/questions/1491/what-should-be-done-with-questions-asking-for-game-recommendations">ultimately disallowed</a> because of the inherent problems that make them unsuited for the SE engine.</p>
<h2>Subjectivity Problems</h2>
<p>The subjectivity of criteria for recommendations is the first problem, which you mentioned, as that very easily skews answers to becoming Not Constructive. When someone asks for a recommendation based on their enjoyment level of an existing work, it is practically impossible to give a canonical answer because of enjoyment level being so subjective from person to person.</p>
<p>If someone really enjoyed <em>Serial Experiments Lain</em> and wants something similar based on X, Y, and Z subjective criteria, how are we to determine what an appropriate, canonical answer is? Even if you look at objective criteria (cyberpunkish aspects, scifi setting, etc.), the determination of a canonical answer is still difficult because the asker may not feel that certain characteristics of another series match up &quot;enough&quot; to their criteria.</p>
<p><strong>Can't we allow them if they're specific enough?</strong></p>
<p>Again, determining the criteria for &quot;specific enough&quot; is incredibly difficult. If one person asks for 5 specific characteristics and another only asks for 4, do we close the one with 4? How vague or specific should said criteria be? This creates confusion for both drive-by visitors and for the community as a whole.</p>
<h2>Inaccurate Voting Problems</h2>
<p>This is a <em>huge</em> issue with recommendation-style questions. Specifically, inaccurate voting issues are when answers end up garnering upvotes based on popularity/enjoyment/other subjective criteria <em>instead of answer quality</em>. This is <em>bad</em>.</p>
<p>For example, when we still allowed these on Arqade, any game-rec question that had an answer with &quot;Portal&quot; in it garnered a large amount of upvotes simply because Portal was mentioned in the answer. These questions turned into impromptu polls that awarded reputation that was not based on <em>quality content</em>, which is ultimately what we want to reward.</p>
<h2>List Maintenance</h2>
<p>While a bit minor in comparison to the above 2 problems, the issue of maintenance when allowing these questions does play into the problems they have. When asking for a series recommendation, any new entries that fit into the (subjective) criteria the asker wants would have to be updated. This creates a maintenance problem the community has to deal with, keeping possible answers up to date in order for the question/answers to remain relevant. Again, this can be a somewhat minor issue, but it can still be a problem, especially considering the propensity for these questions to be asked in high volume.</p>
<h2>So what do we do?</h2>
<p>Using the associated chat room is a good solution for areas of interest to the anime/manga community that can't be dealt with/aren't appropriate for the site proper. While some suggest a separate recommendation room, based on experiments with a separate game recommendation room in the past, I would suggest directing people to the main anime/manga discussion room, as it will likely have the most activity. Making people go to a recommendation specific room may not be fruitful at all, as it depends on the number of people willing to hang out there and <em>only</em> talk about recommendations. We've found on Arqade that directing them to our main chat room has netted the best results.</p>
<p>In addition, once the site picks up in traffic, we may be offered an Anime blog sometime in the future, which is also a good place to list more permanent resources for subjects like this. You could even do a recommendation-a-week blog or something like that!</p>
 -1: <p><strong>Absolutely not.</strong></p>

<p>I've been a longtime lurker on the Stack Exchange sites (notably, SciFi) and I can say that these types of questions are <em>always</em> not constructive. </p>

<p>The <s>Not Constructive</s> "off-topic" close reason has the following text appended to it:</p>

<blockquote>
  <p>As it currently stands, this question is not a good fit for our Q&amp;A format. We expect answers to be supported by facts, references, or specific expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, see the FAQ for guidance.</p>
</blockquote>

<p>Questions that ask for anime recommendations are:</p>

<ul>
<li><strong>Not empirically answerable.</strong> -- They don't have one, or even <em>finite</em>, correct answers.</li>
<li><strong>They're flamewar bait.</strong> -- People <em>will</em> get into comment-fights about which anime is better, which is the better recommendation, why someone's rec was wrong, etc. I don't want to see that kind of drama here.</li>
<li><strong>They're usually polls.</strong> -- A non-terminating list of answers that get votes by popularity? Classic poll. Plus, mainstream titles (Naruto, Bleach, One Piece) are going to get more attention than less mainstream / niche shoujo or seinen/josei titles (Sainkoku Monogatari). </li>
<li><strong>They're an excuse for discussion.</strong> -- Good recommendations will require extensive knowledge about the OP's tastes and likes/dislikes. This is better done in chat.</li>
</ul>

<p>Basically: <strong><em>always close these questions as <s>Not Constructive</s> "off-topic"</em></strong> and hold these discussions in chat instead.</p>
