I married Lydia, and gave her the Archmage's Robe to wear. She will put it on when she is following me, but when I send her back home she is just wearing nothing when I return. Is there a way to make her keep it on even after I leave?

Well I think the way followers work is that they use whatever they will make the most use out of. Lydia's a melee chick so she'll use heavy armor.

"hello honey, welcome home! Now... unwrap your present dear!"

Just kidding...

To make companion/s wear an armor item ALL THE TIME you have to remove all armor and give them only the armor you want them to wear.

Followers revert to their default clothing when they're at home, but when they follow you back outside they'll be wearing the most effective armor and weapons in their inventory.

Also
haaha well you are married to her

Haha, it is a comical situation! I should appreciate the fact that she is wearing nothing when I return home, but alas I would like her to wear the nice clothing! Is there no way to make that her default equipment? Or will she forever take off whatever I give her after I send her home?

Is she walking around in her original steel armor, or is she walking around in her underwear?

She's walking around in her underwear, but this is because I deleted the Steel Armor from her inventory. So I guess my ultimate question is, can you change an NPC's default clothing? Or force them to always attempt to wear a specific piece of equipment?

They never wear the stuff you give them after they leave your services. You have to have them follow you again, and then initiate a trade with them, then they'll keep it on.

I don't know why, but that's how it is.

As others have said, it depends on the character. I've only used Lydia as follower, but from what others have said all followers use equipment that matches their perks - and Lydia's a tank, so she's likely to put on the best heavy armor available to her.

I assume you're trying to get her to wear the ultra-cleavage-emphasizing dress the chicks in the taverns wear?

I've used the console to remove everything from my wife's inventory and then give her the stuff I want her to wear. Of course, this only lasts as long as I'm in the cell. If I leave the house and then return, she's magically spawned her old clothing in her inventory and switched out the stuff I gave her.

Haha, I'm having her wear this...

http://www.skyrimnexus.com/downloads/file.php?id=2688

But of course she won't keep it on after I leave. There has got to be a way to change their default clothing!

Well, holy hell, of course she isn't gonna wear that around the streets of Whiterun! You probably have to promise to do the dishes for a month just to get her to wear that in the bedroom. She couldn't wear that around a bunch of Vikings Nords without carrying an Uzi wherever she went.