I've performed several usability tests, mainly with one participant at a time. However, I have never tried to perform a usability tests when you have e.g. two persons cooperating on a task.
Multiple user testing is generally utilized in collaborative projects. Multiplayer games, source control applications, social networking, etc.
Many times, it requires users to perform different roles simultaneous that affects the application working. There's this one music site (can't remember the name) that allowed musicians to take live requests from an online chat room. Naturally you would need a musician and a spectator simultaneously to verify the usefulness of your interface.
Projects which require long term involvement of the user can benefit from varied experiences of multiple users. If a single user were to participate in long-term usage, they would tend to stick to a particular method of making their way about the application. This is not really beneficial when you want to weed out potential problems in your interface.
References: http://www.nngroup.com/articles/multiple-user-simultaneous-testing/
To me, it depends on the purpose of your app/site etc. If the goal is to achive something by yourself, testing should also be done with one participant at a time. Using more that one participant coorperating will give very different results, as theoretically with 2 participants only 50% need to know how something is done to ultimately get a 100% score.
Even worse: because they are cooperating they can feed of each others ideas and observations, both achieving more that they would indivually do. For example: examine this scenario:
Person 1 (p1): I have no idea what to do
Person 2 (p2): What if you click here?
p1: Hey that works!
p2: All right now I have no idea
p1: What is you slide this to the right?
p2: Yes that is the solution!
In this case, individually, neither would complete the test, as p1 would be stuck at the first step, while p2 would be stuck at the second step. That could lead to the conclusion that the product needs a lot of work. However if you just look at the results of the collaboration, your instinct would say that everything is working perfectly as they both achived the goal!
The negatives I've experienced:
The positives:
People sometimes expose more in a conversation than they do with think aloud. I think the example scenario that @user1261104 gave in their answer is actually a great example of this. By listening to the problem solving conversation between the participants it becomes very clear where problem spots are.
I've had a couple of experiences of it helping get more from sessions where the participants have status / safety issues with respect to the moderators. For example we did some testing a while back with teen and pre-teen women around a pretty sensitive topic. Testing with pairs of friends really helped produce a lot more useful info because they were much more at ease.
Especially when you're doing non-lab testing you'll discover that many situations that you nominally think of as being single-user tasks actually involve multiple people. For example I've seen several occasions where the person making the buying decisions on a web site is making the purchase in co-operation with a more technically savvy family member who drives the web site.
Some products are naturally multi-user (chat, games, etc.)
Very occasionally recruitment costs / participant availability / scheduling constraints means that having multiple participants only way you are going to be able to work with a set of participants.
For me the negatives generally outweigh the positives. Especially when having more participants per-test means fewer testing sessions.
