Hello there,
as a long time WoW player, there are a few functions I would love for Garrisons to have.
First of, the "Guest book".
Battletags of friends can be entered here and will allow players to visit your Garrison at any given time as long as their battletag remains in the Guest Book. The problem of entering your own and a friend's Garrison can easily be solved by adding a tiny menu. This menu could be summoned by right clicking your own Avatar and it would say "Garrison:" and then drop down the names of your own and your friends' garrisons that you are registered for through their guest book.
The Guild Garrison
Not only does the Guest Book function already lead to the next bigger picture, but it also leads to an easy jump to include guild members in to the list. Meaning, if someone decides to add their guild to their Garrison, the whole guild will be able to enter it as long as they are in the guild, offering an easier access method than through entering Battletags by hand.
Outdoor Customization
Instead of only having the choice of where to place a tower on which plot, give players to move small things, may it be statues, flower pots or even benches to some locations that do not interfere with NPC walkpaths.
Extended Outdoor Customization
Optional land plots (size small to medium maximum) would be perfect to have things such as a small inn or maybe even a statue of Malorne if that tickles your fancy. Or maybe just a hut with a big ol' bonfire in the middle and a bench around. You know, RP stuff. Or maybe a fountain here and there, its gotta look pretty, even in times of war, right? Its out Garrison after all. Maybe you have a dummy range where your Instance-NPC's train and you can test your own DPS. Lots of potential.
Exchange of colours
As I am thinking about the garrison, I am thinking a bit of stormwind, ogrimmar. Flags everywhere. Give the players the ability to choose their own flags. I mean with that. A troll player could choose to have Sen'jin flags and Horde flags mixed. Or a Gnome player could have the place have all the alliance flags exchanged with Gnomeregan flags. You get the idea, make it possible for players to replace graphics a bit that are very easy to replace, one of many examples: flags, tabards on NPC's, etc.
This does however not stop there. Maybe players should have the choice in the colour of their buildings' roofs and maybe even the colour / structure or style of certain things, such as the streetbricks etc. Idea by
Narbootz
Non pet battle pets
Quite easily described as creatures that you happen to find in the wilds, anywhere in Draenor or maybe even Azeroth and bring back to your Garrison. They could have interactions with other pets, chase them around, interact with certain followers and maybe even have their own little gimmicks here and there such as finding flowers for you to place and plant in certain areas, or maybe they'll just bring back something that could be moderately useful every few days. Anything goes here basically, a bit opportunity to personalize the Garrison and give it even more of a "this is my place"-stamp. Summed up from
Diaskeaus' post.
Emblems
The idea is basic. Instead of entirely changing the flag from Alliance to Exodar for example, the Emblem concept would let you choose from the guild emblems and apply them to the tabards / banners, etc in the garrison. Idea by
Mysticx
Cosmetical item drops
As simple as it sounds. Item drops from virtually anywhere that are themed after an instance or certain encounter that can be acquired by re-doing the old or doing the new things. (For example like the Sha goo-pet from SoO and the imp from molten core) Or like Trophies you can hang on a wall (think Terraria). Idea by
Bigthumbb
The Arena
The Mists of Pandaria Proving Grounds Arena was very imposing, however far away. it would be very nice if we could have our own secret underground arena right under our garrison. Why under? Well, this is to avoid having that huge building in the way after the player reacher gold in all places. Idea by
Zeror
The Pawnshop
So the owner of the Garrison had a lot of stuff she/he certainly wanted to get rid off. However, instead of just getting those 2 gold coins for the expensive ore that you find on the AH for 9001G per stack, you visit your friend's pawnshop for his price at his conditions. This is a shop, much like the black market, where the NPC sells the things and the Garrison owner can give the NPC the things he wants to sell. At the end of every week, the pawnshop sends a mail of summed up sales to the Garrison Owner. Idea by
Zeror
Hope this sparked your interest, I may add more ideas as they come to mind and I would love to add community ideas to this "list"