Does a house trailer increase in value over time like a house, or does it lose value over time like a car? Either way, how much does its value usually change over time?

It loses value because it is real property not real estate. Doesn't matter if it has moving parts or not...it's not connected to land (real estate).
It can be removed from the land just like a vehicle, or an appliance or any of the items in your home.
If you own the land the trailer is on, that is real estate and that will (generally) increase in value over time.
If you remove the wheels and build a fixed foundation and afix the trailer to it...in some jurisdictions, it may be classified as real estate.

Generally a trailer depreciates but the situation is highly dependent on whether it is on owned or rented land http://ezinearticles.com/?The-Truth-About-Mobile-Home-Appreciation-and-Depreciation-for-Real-Estate-Investors&id=134154 .
If a trailer is kept on a rented lot in a park for long enough, its condition may very slowly deteriorate to where it cannot be moved and it would have to be abandoned or scrapped if the park were to close.

They depreciate. The change in value of the home has many factors, age of the home, upgrades, location and land rent are the big ones that determine the homes value.

It loses value because it has moving parts. Even new ones lose value because of this. I'm not sure how much value it loses, but I believe it is comparable to a car.

I'm not exactly sure, but I believe if you put it on a sturdy foundation (like one for a house), it does not lose value, at least not as quickly. If you're thinking of buying one, especially one new, I'd recommend doing this.

Read the end of the history section here: http://en.wikipedia.org/wiki/Mobile_home for more information.

A house trailor is worth the land that it is on. A trailor does not have a foundation so it would be more like a car in that it depreciates in value.

They lose value

if it can be avoided...do not live in one...

Probably decreases in value. First of all, not all houses increase in value, if you've been watching the news in the last year. Realistically you are probably best off trying to maintain the value of the trailer by taking good care of it.

I own a single wide trailer. Even with upgrades, I have been told the value de-creases. Atleast in this area. I think it might depend on where you live?

They drop like a rock. I bought one new in 1995 and sold it eight years later for $12000. I paid $26000 furnished. I kept the furniture which was maybe $1000 new. I then bought a 1997 which was bigger than my 1995 and got it for what I sold my 1995 for...they lost $28000...and neither my case or theirs includes the loss of interest paid or the lot rent paid. Still, it is about the same overall as renting an apartment. If you stay and do not sell, at least you have your own home. That means something to me. Still, you have to do maintenance and repairs on it if you own it.