I suppose the "driest" meaning of memory is to do with memory feats, memorization etc. You could mention mnemonics, the "keyword" technique etc to your students, but you might bore them (I bet they have had enough of memorizing endless vocabulary lists!)...see the "association" activity in 2) below for something a bit more fun.
1) Ever played something like
"The Shopping Game"? A: I went to the supermarket and got some apples. B: I went to the supermarket and got some apples and a bottle of wine. C: ... (but I think this is a bit boring).
Chinese whispers isn't exclusively to do with memory (the whispering and laughing helps garble the message more than anything else!), but it could shed some light on the limits of auditory memory.
For visual memory: what's the name of the game where you show a table full of items, and then remove something and the students try to remember and guess what is missing. Is it called
"Kim's game"? (To prevent cheating by peeking students in class, you could take mpegs of a some stuff at home, if you have a digital camera, and give students "before" and "after" pictures). You could also get them to remember the differences between "Spot the difference" pictures after they've spotted the differences and you've collected the pictures back in.
2) One game I like to introduce this idea of associations is
"The Colour/Memory Game". Divide the class into two halves, and ask one half (A) to think of a colour. The other half (B) then has to think of something associated with that colour. Play then passes back to the A half, who have a choice of thinking of something new associated with the colour, or of something associated with the word that the B half came up with. You would be boarding this stuff much like a "mindmap".
The basic game is just coming up with words, but if memories associated with any words occur to anyone, they should feel free to begin telling others about that memory (usually in the form of an anecdote or a bit of trivia, or a question). Things can get pretty crazy with this game!
Some examples: A - white; B - snow; A - ice; B - You know, quite a few people in Hokkaido get killed by blocks of ice falling off their roofs. I had a narrow escape once myself...
A - orange; B - carrot; A - rabbit; B - Hey, have you ever seen a movie called
Shogun Assassin? There were these lady ninja in it with throwing knives hidden in their carrots... (I told you this game could get crazy!

).
The associations that people come up with can be quite revealing about their interests if not their outlook on life! This game also goes by the name of "Psychologist's couch".

It can be a good way to hit upon an unexpected yet interesting topic for discussions.
3) There's a Japanese movie (that I haven't seen, and can't remember the title of) where people who have died and gone into the afterlife are interviewed by a counsellor about their happiest memory. The memory is made into a movie that will accompany them into eternity (they kind of go on living (in?) it forever I guess). You could easily ask students about best/worst memories.
One question that is often really hard to answer is: Have you ever forgotten (to do) anything (that was important, or had e.g. bad or embarrassing results for you, or somebody else)? It seems we remember our successes, but are more liable to forget or gloss over our failings!