Other than the obvious differences in appearance, and the difference in starting attributes for each race (covered on the Races page), there are few differences between male and female characters in Morrowind. This page lists the major ones.
This female Khajiit living in Pelagiad has a whole series of quests - but only for male characters. Most of the items she sends you to retrieve can be found with a female character as well, but you have to know where to look for them, as nobody will tell you.
Mistress Dratha is a Councilor for House Telvanni, living in Tel Mora. She is very biased against men, and won't even allow any to live within her city. For the few quests that involve her, you'll have a much easier time if you are playing a female character. The quests are:
- Telvanni Hortator - As a male character, you will need to raise her Disposition to at least 80 in order to even talk to her. This can be difficult if you happen to be a member of one of the opposing houses or the Mages Guild. Even with this higher disposition, you'll need to hurl yourself at her feet and beg to be heard. A female character will be accepted no matter what.
- Flesh Made Whole - Only an issue to members of House Telvanni, but you will receive an extra reward of 4 Scrolls of Summon Golden Saint if you are a female character. Additionally, if you choose to kill her afterwards in order to retrieve the amulet, a male character will be disappointed, as she won't have it.
This bandit found on the road near Pelagiad will demand 50 gold from you if you are male, and if you don't give it to him, he will attack you. If you are female, you can get by with a kiss. Or not - even if you don't, he won't attack you, though he'll be somewhat disappointed.
This Breton Noblewoman who had a run-in with a thief in the woods west of Pelagiad fancies herself something of a matchmaker. In exchange for you helping her reconcile with said thief, she will attempt to hook you up with a friend of hers. If you are male, it will be Emusette Bracques at Plot and Plaster in Tel Aruhn, and if you are female, Barnand Erelie at Sethan's Tradehouse in Tel Branora. Either way, the reward is the same, and there is no way to actually pursue a romance with either of these people.
During the Disguise quest for House Hlaalu, you will be asked to wear a helmet and disguise yourself as a fallen Redoran warrior, in order to steal some secret orders from Neminda in Ald'ruhn. If you are male, your assumed name will be Felsen Sethandus, and if you are female, it will be Relmerea Saram. (If you are Argonian or Khajiit, this quest is unavailable.) Either way, the rest of this quest is exactly the same.
There are very few other differences, most of which just involve different pronouns or terms of address being used in dialogue. Faction rank names all generally assume you are male - "House Brother", "House Father", "Swordsman", etc. The dancing girls at Desele's House of Earthly Delights in Suran will behave differently based on your gender, offering you either a job or a good time, depending. In other cases an NPC's interested behavior does not change based on the player character's gender at all. For example, Bosmer with a very high Disposition to you will seem to be very enamoured of you either way and Crassius Curio of House Hlaalu will call you pet-names, request to see you naked, and ask for a kiss whether you are male or female.
Everything else is just cosmetic. Certain armors and clothing (though not all) look different depending on gender. (Most unisex armor and clothing looks generally male on either gender, though the armor added by the LeFemm Armor Plug-in looks female even when worn by male characters.) Height and weight may be different. This does have a side-effect of altering Speed - Heavier characters are slightly faster when walking and running. Shorter and thinner characters can fit into places where larger people can't - though there's very seldom any need to do so, as pretty much all locations that you'd ever need to go to are designed such that any character can fit through them just as easily. These differences are covered on the Races page. The total for all of the Attributes adds up to the same value regardless of race or gender, so you won't max out your stats any earlier based on these factors.