If we’re going to adopt a gender-neutral substitute term (and I think we’ll need to, someday), we should avoid confusion. The new term shouldn’t be a homonym for already-existing words like “her” or (almost) “him.” It should be something distinctly new that clearly means something new, IMHO.
There are at least two pronouns which work with this example, which are gender-free, and which satisfy the most old-fashioned grammar purists:
When you go to class you need to bring your syllabus.
When they go to class they needs to bring their syllabus.
(For the second, assume that the discourse started with a reference to “students” rather than to “a student”).
If the matter is actually intended to be read by students, then the consistent use of “you” makes is a lot more readable.
Er…?
“When they go to class they need to bring their syllabi.”
Or “syllabuses.”
Buseses… es.
…es.
Whatever.
Yes – “need”, not “needs”. However, I’m not sure that “syllabus” needs to be made plural: each student only needs to bring one with them.
(Yes, I do practise the singular “them” on occasion myself).
And we are all forgetting the wonders of “one”
When one goes to class, one must bring one’s syllabus.
(eyeglasses on the tip of the nose optional)
This could be confusing if one of the classmates is called Juan, though.
Why is “their” improper? They and their are perfectly fine gender neutral constructions that have been used for centuries. What makes them wrong? That they’re also used as plurals? Who died and became God and decided that they couldn’t be singular?
This is what everyone should do when they are writing. It’s perfectly fine and when a person reads it they will understand perfectly. There is no need to construct an artificial gender neutral singular, such a thing already exists and only prescriptionist nazis will tell you otherwise.
Huh; I get this response every time I say this. It has long been accepted usage in English to use “it” for a human baby of unknown or unstated gender.
While it’s technically considered “improper” to mix plural and singular, there is growing acceptance of “they” as a gender-neutral third person pronoun, even in the singular. Bear in mind, it is not acceptable in scholarly papers, literary journals, term papers, legal documents, and so on, but in ordinary communications, I don’t think most people would call you on it.
Fair enough. When it’s not known.But are you going to go to a resturant on a date and say “I’ll have the shiraz and it will have the pino noir”? You’ll end up covered in pino noir.
Well, perhaps you might end up covered in pinot noir. Not sure quite what you’d end up covered with if you don’t like the letter “t”. 
Actually, she prefers margueritas.
The point of this thread was to come up with a gender-neutral replacement for he and she. “It” is, in my mind, the perfect replacement; it already exists. But as you and others point out, it seems that no one can bring itself to use the term. Me included.
It puts the pinot noir in the basket or it gets the hose again.
I did a little proofing for a magazine yesterday and his or her popped up three times in one short paragraph. There is no happy Doper solution yet, but I did take a cue from Ms. magazine. I rearranged the order: her or his. It’s still frustrating to have to use both of them, but at least it gives us a change from the standard fare. My editor liked it.
Of course that’s exactly the same problem we have right now. the term ‘he’ can mean ‘he’ or ‘he/she’. The term ‘they’ can mean ‘they’ or ‘that person of unspecified gender’, the term ‘it’ can mean ‘it’… well, you know the rest.
The English language doesn’t have a suitably neutral word at the moment, so we have five choices:
-Invent a brand new word - say, ‘snoo’ that means ‘he or she’, but people won’t use it because a brand new word in such common need of use seems too silly
-Coerce another word to serve - say, ‘it’, or ‘they’, but that won’t work because it brings existing meanings with it, and the misunderstanding offends and confuses.
-Keep on using the generic ‘he’, but that’s obviously no good, hence this thread.
-Reword everything so as not to require a specific term (for example change “each passenger is responsible for his/her own baggage” to 'passengers are each responsible for their own baggage") - but sometimes this is hard work and sometimes makes for long and awkward constructions.
-Keep on saying ‘he or she’, ‘his or hers’, etc - awkward, but it works
Presumably, when you are a date with a person, you know their sex or gender identity. It’s only for cases where you are talking about a singular person, but don’t know their sex or gender, that you need a pronoun other than “he” or “she”.
I like the solution of the WotC D20 manuals: alternate examples. In the first concrete example where a generic pronoun is needed, use male (or female.) Then, in the next example, use the other pronoun, and alternate thusly. (Probably wouldn’t work in a short article, even with several examples, as people would read too much into the “gender roles” implied by assigning different genders to different examples, but if everyone adopts this usage it should be clear that no such stereotyping is going on.)
Even that might be misunderstood in some circumstances; a person of one gender dipping into a company procedures manual, for example, and finding a paragraph that happens to use the pronoun for the opposite gender, might mistakenly think it doesn’t apply at all.
I’m happy to be guided by the example of Word Maven[sup]TM[/sup] William Safire, who wrote more than once, “If anybody asks [who approved this construction] tell them it was me.”
(Actually, the construction referenced was the “it was me” part, but the pronoun slipped by so smoothly and naturally he never caught it.)
Go Word Maven! 
What if we have a compromise, and males get one of the pronouns and females get the other?
For example, let ‘he’ always denote he/she, and let ‘her’ always denote him/her [sup]1[/sup].
The words already exist, and the above scheme prevents the silliness of using ‘he’ in one paragraph and ‘she’ in the next.
A sample sentence:
“Someone went into the copy room last night. He must have been very drunk. When I find out who it was, I will give her a stern warning”.
[sup]1[/sup]Or, let ‘she’ always denote he/she, and let ‘him’ always denote him/her