For some components, unit tests are done, but to be honest the parts are few and far between (maths libs, input, etc).
Ad-hoc corner cases finding, the coders can predict certain areas they suspect bugs lie (loaders, tools, graphics, networks) and delibrately stress test them (i.e. build test models, pull network cables etc).
Their is also internal iterative testing, building the game means alot of data will pass through our hands, their is usually a "shout if it breaks" policy. These either get added to internal TODO lists or fixed on the spot (you can tell when this happens the usually unmoving programmer gets up, moves to an artist's machine and then comes away swearing that can't possible happen).
Then their will be external 'proper' testing, a QA team will play the game, test installer, for PC hardware compatiblity labs (computers set up with various combination of hardware/PS), etc. This bugs will be entered into a database, fixed by the devs (could be an art , design or code bug), then re-tested before being closed. At this stage bugs are classified with A being bad, generally no game can ship with a class A bug. Before any bug can be ignored, it usually has to be signed off by the publishers producer.
When the publisher is happy (or deadlines have been over ran several times,
) the game will either be shipped (if a PC title) or if a console title go into submission.
Submission brings dread to any console team, as here the console owner (Sony, Nintendo, MS, etc) hammers the game to make sure it meets their own standards. Things like saving have to meet exact standards, often the standards doc (currently known from the Sony name of TRC's) have pages of details that you have to get exactly right. Also they will test to try and make it crash etc (Things like running it constantly for 72 hours to make sure things like memory fragmentation doesn't affect it). Usually you fail at least once, which causes a resubmit which may delay release for 6 weeks.
The harsh submission is why console titles have much better quality standards then PC tltles, I've seen publishers ship games with some terrible bugs on PC, whereas on console even minor bugs usually have to be corrected as they know they can't get away with it.
For a game they only really successful test strategy is to play the game over and over again, often not to win but to test. Things like walking into every wall to test collision, saving everwhere, doing stupid things. We usually have a number of aids that allow us to jump anywhere and test that area.