Most folk agree that writing he/she is a pain, however, nobody agrees on what is the best substitute.
Singular they is the most commonly used and it appears in the king James's bible, so when Jehovah speaks English he/she uses singular they (ref). That last sentence shows that it has a glaring problem: singular they is used as a plural and the closeted prescriptivistic pedant (†) in all of us screams out upon hearing a grammatical number mismatch (e.g. "Someone has made a mess again, I wish they'd tidy up once in a while"). "They is" is too revolutionary to be anything but jarringly awkward sounding.
Impersonal one (from the French homme curiously) is used differently, so is not a gender-less pronoun.
Wikipedia has a hodgepodge collection of attempted pronouns (link), some of them badly put together.
I thought I'd make up my own.
What did the vikings ever do for us? They gave us useful words!
They in English is not of Old English origin, but of Norse.
The third person personal pronouns in Old English are: (in the order subject, possessive, direct and indirect object)
M: he, his, hine (=him), him
F: heo or hie (=she. eo is read ee), hire (=her), heo or hie (=her), hire (=her)
N: hit (=it), his (=its), hit (=it), him (=it)
Pl: hie (=they), hira (=their), hie (=them), him or heom (=them)
As you can see, not only some forms are repeated within a gender as in in English (her can be possessive or object), but also between (him can mean to it or to him). Therefore the Norse they makes life so much less confusing.
Humorously, hie could be they or she, which would make gender-neutral pronoun advocates happy.
Search the Old English 3rd prs. plural pronouns gives me:
hie became hi or hy, which was last used in 1400.
hera gave us her.
heom became hem and then 'em.
So one version of a gender-neutral pronoun could be:
hy, her or heer (modernised hiera), hem or heem (modernised heom).
Hy sounds a lot like I, though.
Alternatively, Old Norse could be the source of the sought pronouns.
The thon pronoun set which someone proposed is not based on the singular form in Norse as only the neuter begins with รพ (thorn, th-group) and it is the same as the demonstrative pronoun that.
The feminine set is: hon, hennar, hana, henni
They have no derivatives in the OED, so hon, hennar and henne could be another set, but they do not sound English.
Those Old Norse pronouns became hon, hennes and henne in Swedish, which has a made up gender-neutral pronoun, hen, which would not work in English for obvious reasons.
Taking a step back, I think I'll adopt hon, heer and heem.
Example: Someone e-mail: hon said to call heem or heer secretary.
Maybe I'll stick with he/she.
†) Prescriptivism may suffocate the natural evolution of a language and has the sole purpose of linguistic snootiness, Descriptivism is a tad hypocritical to say the least. Descriptivistic snootiness at prescriptivistic snootiness at grammatic butchery...