Nearly anyone who has experience raising goats will tell you that a shelter is very important. Perhaps even more important than fencing. And in my travels and talks with other goat people, I have heard of and seen a large variety of shelters - some prefabricated, some makeshift - but all of them essential and functional. 
Okay, so you're asking, "why such a big deal about shelters". They are just goats and goats live in the wilderness don't they?" Yes and no. While goats as a species do come from the wild, they still have an instinct to seek shelter in inclement weather. And one must remember, goats that are raised by humans are primarily domesticated. They do lose a bit of their "wild" instincts in captivity. 
For the most part, what you are trying to accomplish with a goat shelter is to protect the goat(s) from the wind and rain and snow. A goat that gets wet will almost certainly become ill. A wet goat in the wind will also almost certainly produce a sick goat. And a key issue to remember is that goats easily get pneumonia if wet and cold, and pneumonia in a goat is a swift killer. So it should be taken to heart that goats need shelter. 
Not everyone has the luxury of a barn where they can herd their goats together at night or during inclement weather. So improvisation is most often the best choice here. But for those that do have a barn or building as such, let's start here because this is really the best, and most convenient to you and your goats. 
The first thing to understand (and it took me awhile) is that goats cannot tolerate as easily sudden temperature changes. -40 degrees outside and 80 degrees inside. Some will argue this but I stand firm because even humans cannot tolerate such temperature differences without some kind of health concerns. So heating a shelter is probably not necessary unless of course a few regular light bulbs to keep the temperature a few degrees warmer are used. Goats, like many other animals such as horses have hollow hair meaning they can withstand some pretty cold temperatures. About -40 for short periods of time. Extended cold - you may run into some problems. 
Shelter bedding is available in many types with perhaps a good grade, clean straw being the ideal. You will want to arrange shelter bedding so that it can be changed frequently as the goats will urinate on their bedding causing it to get wet underneath and it is usually this moisture buildup that breeds harmful bacteria that can lead to health problems. What I do is arrange the shelter bedding on slatted pallets so moisture drains through underneath and does not remain on the bedding itself. 
It is a good idea to change the bedding frequently to minimize bacteria and parasites such as lice and worms. Personally, I gather all the soiled bedding into a large pile, let it dry and then burn it. The soiled bedding could also be used for compost as well. But in our case, it is easier to burn the goat pen areas to decrease harmful bacteria. While this is not always possible for everyones circumstance, it has been quite helpful for us. 
Some breeders employ "listening devices" in their goat shelters so they can monitor their goats activity at any time of the day or night. Unfortunately we haven't gotten this "hi-tech" yet, but it is a great idea that costs around $50.00 for a good intercom or "baby monitor" system. You can listen in on your goats or an expectant doe who is getting ready to kid. 
A goat shelter can be as basic or as elaborate as you wish to make it. Shelters that we use are of two types: calf hutches and a homemade goat shelter built from cedar shingling. The calf hutches are very nice because you can attach cattle or hog panels on the front to complete the enclosure. In essence they become small goat pens, easily movable. These hutches will hold about 10 full sized goats and come with side feeder doors, a top ratable open/closed air vent, a front feeder/waterer holder and two inside the hutch feed and water bucket holders. The price of a new hutch is approximately $350. Do yourself a favor and buy used but be sure it is in good conditioned and not cracked or broken. 
The other home made cedar shelter is pretty nice as well although not as movable. It is roughly 4 feet deep, 4 feet high and 6 feet wide with corrugated tin roofing and 6 inch deep walls packed with R-14 insulation. The floor is two pallets with straw strewn over. Originally built as the "yard" kidding pen, it has provided a shelter to many of our goats from time to time. There is one drawback to this particular shelter - our goats love to gnaw on the cedar boards. 
One other plan I have had in mind for a long time is a "range shelter" built from cinder blocks. This particular design would be a concrete floor* and the dimensions would be at least 6 feet high, 12 feet deep and 24 feet long. Running water would be piped to this particular shelter. The roof would be corrugated tin on a 7 point pitch to adequately channel rain water to the back of the shelter and not the front. Also, this design would have a door on both sides. 
You'll notice that I asterisk (*) concrete floor. I have always heard that concrete has a tendency to hold moisture and will drain energy out of an animal through its feet. I may opt to go with a different material over the top of the concrete floor but it will be built so as to house drains at various points in the shelter to make clean-out easy. 
A quick note about "wooden" shelters. Wood can be and is used quite extensively for the DIY (do it yourself) shelter maker. One word of caution here however. I would be careful on the wood type - certain woods splinter more easily than others. Certain woods also attract goats to gnaw away until the wood is gone. And painting the wood - be very careful of the type of paint you use. While most of the lead based paints are gone, there are other ingredients that can make your goats sick. 
Another type of range shelter most often employed not only for goats, but cattle or horses as well is an open faced, three sided shelter constructed from corrugated tin. These usually work quite well but the open front has always concerned me a little. If you live in a place where the rain comes from any angle, your goats are still going to get wet. I am thoroughly convinced that a goat shelter should be closed enough to ensure that the goats remain dry no matter how hard the downpour is. 
A couple of other ideas for shelters - "pet Igloos" like they make for dogs. These work great for kids and smaller goats such a Pygmy. The "portability" of a shelter is quite often a real concern (see the fencing topic). 
The "strangest" shelter that I've ever seen and worked quite effectively is a concrete culvert pipe - you know the big, round water pipes that are put into ditches? I actually saw a guy use a 20 foot culvert pipe for a shelter. Great idea and works well until it's time to get the goats out of the pipe when you need them. I thought about this idea and wondered if a metal culvert pipe would be better. No. Metal gets cold in the winter, hot in the summer. Concrete is a little better than this although not ideal. A culvert pipe with straw bedding will suffice. 
Other Shelter Ideas
Bearing in mind the cost of materials, etc., I was contemplating what we could do to build a barn. Here's what we did: My husband was at an auction sale where he purchased a 48' van (like the one's you see going up and down the highways). He knocked the under-carriage out from beneath it, put skids under it, and hauled it out into the goat pasture. It has a really solid, wooden plank floor inside, wooden walls, and of course is completely covered in tin all over the outside. There is a very large side door as well as the big door in the back of the van which makes for very easy cleaning. Absolutely waterproof with no maintenance required because of the tin covering, and I leave the side door open so that the herd can come and go at their leisure. We use lots of straw for bedding and have it positioned in the pasture to maximize the sunshine and yet not allow the wind to carry moisture into the barn to make it pretty much draft free. Cost: 650.00 (Canadian) and a bit of work to customize the interior into 2 pens and a milking area. I find it ideal for the herd in general but I also have 5 small pens for kidding or isolation use. Not perfect perhaps, but better than nothing, right? 
I started with my two little goats and an 8'X10' pre-built shed. It was made by the Amish, and delivered to my site. It worked fine...until I decided I needed more goats...then I needed more barn space, especially since I had two bred does, and two new kids. Sooooooo, I haaaaad to get another barn....back to the Amish. This time I got a 10'X12' and my husband and I divided it to serve as temporary kidding stalls when needed. Thennnnnnn, I decided to get a billy goat. Well, I couldn't have the billy live with the girls, so yes, I needed another barn. This time my husband and I built a little barn about 4'x8' with a height of about 4 feet. Everyone seems to be happy with their setups. But, if it continues like this, I'll be having too many little barns. So my plans for the future are to buy a nice, big Amish barn to put on this new pasture. So my advise is - if you're just starting out, get something bigger than you think you'll need, as goats are addicting, and you can never stop with just a couple. 
There was an old chicken house on our property when we bought our little farmette 3 years ago. We decided to clean up and convert this little building to become the goats' shelter. It has really worked out well. It is raised and has a wooden floor. I use straw for bedding as well. It is approximately 10'x12', easily big enough for our two pet goats. There is a little cut-out door with a walking plank to their outdoor fenced-in play area. In severe weather, I can close this door and keep them inside. There are also two windows (reinforced w/screen) which can be opened or closed according to the weather. They also have a shelf for sleeping/playing. The best part is, the goathouse is divided into two parts, so there is an additional storage area where I can keep some hay and a can of feed and my broom/bucket/rake for cleaning the pen. A full size door opens into the goats' area for easy and convenient access. 
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