Lodging

Short Term Lodging Options

Hostels, hotels, and home stays are the options in this category, apart from crashing on the couch of a stranger in a foreign country; the latter option is not typically recommended.

Backpack Europe - Information on and bookings for hotels, hostels, camping, and other opportunities.
Hostel World - Hostel bookings and links to city guides, pubs, clubs, podcasts.
AllStays.com - Information on and bookings for hostels and other lodging.
Airbnb - Wide range of housing options and locations all around the world.
Homestay.com - Find homestays near your location. Each home has a host who will help you settle in, which is different from airbnbs or hotels.

Longer Term Lodging Options

Short term apartment rental for stays of one month or more in duration.

Investigate regional physical and online bulletin boards. Craigslist has some international listings. Check any local universities for online postings as well as local newspapers and other community sites.
Universities may allow you to rent their excess housing to you for longer durations.
International Home Exchange Network - Listings and arrangements for exchanging lodging with other individuals. Also has rental listings.
AmberStudent - Site that helps you find housing options near universities and colleges and takes you through the process start to finish.
Airbnb Sublets - Monthly rentals from airbnb. Good thing about these are that they're usually furnished and come with utilities already.
Uniplaces - For housing options in Europe only.
Study Abroad Apartments - Student accommodation options, but only for 13 global cities, so check if your city is listed.

Things to keep in mind

Ways to reduce housing costs: find a roommate, find housing further away from trendy areas (less money spent on rent, more time on public transportation).
Read thoroughly through your rental contract and ask study abroad advisors if you need help.
Landlords are obligated to provide a means of fire escape, smoke alarms on each floor, and any necessary massive remodeling. They also cannot evict you without a cause.
To avoid rental fraud: wait to transfer money online until you are sure it is a trustworthy site, ask someone trustworthy or even the university to check out the housing before booking, ask for separate copies of the tenancy agreement and any safety certificates, and preferably don't pay in advance until you have the accommodation and a key that works.
Often the school you are going to will have options for accommodation you can look through. You can also ask current or former students of the program for any advisement.