I have minimal space under my bed as well and I find that ornament boxes work (remove the inserts):

http://www.containerstore.com/shop/movingShippingStorage/holidayStorage?productId=10014032

I also use these the large sweater bags since they don't have hard corners:

http://www.containerstore.com/shop/closet/storageBags?Ntt=storage bag&productId=10000162

There is almost always something at container store!

I bought cloth sweater bags without an internal frame and just sort of shoved them under my old malm frame. So long as whatever you're buying doesn't have an internal skeleton, if it's 6" tall you should still be fine. Just takes a bit of shoving.

When I had this bed I bought those giant sized zip-loc bags and filled them with clothes. Not as nice as a hard case but it fit!

I used to have Ikea Samla bins under my bed. They exist in a very flat and large size...don't know anything about measurements in inches,sorry. This is the dutch Ikea link:

http://www.ikea.com/nl/nl/catalog/products/00130129

I have this bed so I know! Especially aggravating when I bought ikea's under bed storage system and it didn't fit. I just don't keep anything under there, although I will now after these suggestions

I have a Malm, and I use a bunch of these: Sterlite Storage Boxes. The dimensions are incorrect on the site, as it fits just right underneath my bed. You can buy them individually at the store to test out.

Ikea sells storage boxes that fit under their beds. Did you talk to them?

I have the same bed and ran into the same frustration. I eventually ended up getting clear soft sided underbed storage bags/boxes. I sometimes have to rearrange things I put in them to get the bags to fit but since I only switch things out twice a year, it isn't too much trouble. The ones I got were similar to these:

http://www.amazon.com/Under-Bed-Chest-Clear-42/dp/B0001V681I/ref=sr_1_66?ie=UTF8&s=home-garden&qid=1271252109&sr=1-66

The Container Store has soft-sided underbed bags. I have one in which I store my off-season bedcovers and sweaters. Because it's soft, I can squish it down if needed to slide it under my Ikea bed.

if you want to save some money, try Big Lots if you have one. they have some storage containers that are low and large and have a lid. I have this bed as well and I've been looking for solutions too!

I also appreciate all the suggestions! I have an old Ikea futon, so I've run into exactly the same problem. The only things I have been able to get under the bed are an old laptop and a cutting board!

It sounds weird but if you don't need a lid plastic kitty litter pans are inexpensive and work great for under bed storage. 5" should be just about right.

Thanks for this. I've got a West Elm bed frame with under bed clearance for storage that's only 4 inches!!

I've come to terms with no storage than changing frames.

I have storage bags, too. But, I took some 1"x4" lumber and built a simple frame; made it the size I wanted. I fixed a vinyl clad 1/4" sheet of plywood (the vinyl makes it easy to clean) to the bottom and put a double layer felt on the bottom side to protect my hardwood floor. I took some scraps from the plywood to make dividers. Lastly, an old sheet with some velcro covers it (it gets dusty under there!)

It's big enough that you can grab it from either side but small enough so it's kind of hidden.

I have a malm bed, and eventually had to give my boyfriend somewhere to keep his clothes. We bought a set of 4" legs and just screwed them onto the head and footboard. It was really easy, and you can barely notice them.

Another vote for the container store. I have the same bed (king size) and use 4 of these.

http://www.containerstore.com/shop/closet/storageBags?productId=10009164

I use plastic underbed storage I found at Target under my Malm bed. They are the same ones as these I found on Amazon (http://www.amazon.com/Sterilite-Ultra-Storage-74-Quart-White/dp/B000MPQ91C/ref=sr_1_4?ie=UTF8&s=home-garden&qid=1271286925&sr=1-4) but I definitely did not pay that much for one! The split lid makes them great since I can access the inside without pulling them all the way out.

One alternative: modify the bed frame to make it a lift-up mattress. Take a look at IKEA's Sultan Alsarp:

http://www.ikea.com/us/en/catalog/products/80098880

With parts mostly available at IKEA and the car 'lift' arms from an auto hatchback (auto parts shop), you can do your own hack to create more storage in almost any bedframe. I expect it would work with the Malm using a little creativity OR bribing someone, who has basic woodworking skills, with chocolate chip cookies. I'll be trying it myself but not until Summer (in the midst of resurfacing walls so my hacks have to wait until then). You wouldn't be changing the look of the Malm since all the working bits are contained under the mattress.

I have this bed too and we found some plastic containers at Kmart that slide underneath. Or (this will sound crazy) but we lift the mattress and access the stuff through the slats. Obviously this wouldn't work for every day storage though.

I have a west elm low bed and I found some container store containers that fit under the bed, but not easily reachable. I store off season clothes under the bed. Twice a year I lift my mattress, also a good time to wash sheets, pull up the slats and go through all my clothing. While I'm at it I give my bedroom a very thorough cleaning. Put everything back together again.

PERFECT SOLUTION!
I have this bed and this is what I found:
http://www.canadiantire.ca/AST/browse/3/HouseHome/StorageOrganization/HouseholdOrganization/PRDOVR~0680921P/Debbie%252BTravis%252BUnderbed%252BOrganizer.jsp?locale=en

Although it says its 6", it's a soft shell so it fits underneath perfectly! However, it is a bit pricey.

I use Rubbermaid "Large Organizing Tray" (that fits in the 71 qt container). At 3.98" high, it fits perfectly!

look what i just found! i think these could be pretty useful!
http://www.officedepot.com/a/products/940361/Bankers-Box-Liberty-60percent-Recycled-Storage/?cm_cat=2000000020

or these...
http://www.officedepot.com/a/products/550455/Really-Useful-Boxes-Plastic-Storage-Box/