This instructable is designed to help you clean up mildew or mold that is often discovered growing on the backboard or underside of Ikea furniture.

Step 1: What Are My Options for Getting This Cleaned Up?

As I see it you have a couple of options...

If the problem is mildew, a grey or white surface fungi, you can probably save the furniture by following this instructable on wiping off the mildew, sanitizing the surface, applying a mildew inhibitor and looking at ways to reduce the moisture.
If the problem is mold, a green or black furry fungi (or "mould" in England) then you are dealing with a much more serious health hazard and are probably better off removing the affected backboard and replacing it with a new backboard, or a completely new unit. You can contact IKEA customer service about replacement parts for your furniture piece. http://www.ikea.com/ms/en_US/homeshopping/missing_damaged_parts.html

Step 2: Tools You'll Need

Before you start please make sure you have the following items on hand:

Disposable gloves
N95 graded mask for dealing with airborne mildew/mold spores
Package of disposable anti-bacterial wipes (DO NOT USE BABY WIPES)
Garbage bag for the used wipes and gloves
Mold control spray (I used Concrobium Mold Control Spray from Lowes)
Optional: Shellac, liquid wax or other water resistant sealer

Notes:

N95 masks. National Institute for Occupational Safety and Health is responsible for the N95 designation. 3M is a well regarded manufacturer of N95 and other respiratory filters.

Antibacterial wipes that contain bleach or other chemical to kill the fungus is critical. If you used baby or sanitary wipes you'll just end up feeding and spreading the fungus with more moisture and food!

Mold Control Spray: You have several choices in mold control spray. We wanted something with low toxicity so we chose Concrobium for its Sodium Carbonate (Soda Wash) and TSP (not listed on ingredients but can be found in their safety data sheet). The Concrobium Mold Control Spray is rated for 3 months and works by putting a "salt" in the backboard material that makes it difficult for the mold or mildew to grow.

Shellac, Polyurethane & Varnishes: I used a polyurethane spray to "seal" the backboard after I was all done and given the number of days it took the smell to dissipate and my wife's displeasure about having done it indoors, I would have skipped this step or gone with liquid wax.

Step 3: The Steps to Follow...

Wear your 3M N-95 mask. Mold spores can cause serious allergic reactions, coughing and inflammation in your lungs.
Wear your disposable gloves. Be sure to avoid touching the mold or mildew to minimize the chance of it spreading. Be sure to use a wipe to clean the gloves if you do directly touch it.
Take the disinfectant wipe and systematically wipe down the surface. Take great care to not smear the mildew or mold into areas that are not affected. Fold the wipe to give a clean surface for each wiping stroke.
Dispose of each wipe in the plastic garbage bag.
Be sure to use a new wipe when cleaning unaffected areas.
Be sure to wipe the entire backboard, even the spots where you do not see the Mildew or Mold. We are trying to kill any spores that may already be there.
Be sure to use disinfectant wipes and not a wet rag. We want to avoid adding more moisture than necessary.
When you are done completely wiping the backboard surface you should throw your gloves into the plastic garbage bag full of dirty wipes and then tie the bag closed and take it outside to dispose of in the trash.
Use the Concrobium or other mildew mold control spray to treat the backboard by spraying evenly.
Use a paper towel to wipe up any excess.
Wait for the IKEA backboard to fully dry. You can use a hair blow dryer or room space heater to speed up this process.
When dry you can put the furniture back into use.
You may need to reapply the mildew mold control spray again in 3 months if your still have a moisture problem.

Step 4: Why It Happened? Mostly Moisture...

After you are done cleaning up you should spend some time thinking about why it happened. This is an important step in preventing it from happening again.

Think about how the environment that encourages mildew/mold growth.

Food. The organic wood fiber backboard that Ikea left unfinished is their food source. You'll notice that other laminated side doesn't have this problem.
Warmth. Homes are heated so I guess it is a given.
Oxygen. Unlike plants, mushrooms and fungi are more like animals in terms of needing oxygen. They need the same air we do, but they go a step further by spreading airborne spores which are a real air pollution hazard.
Water. Like us they need water. If you have high humidity you will have problems. This is probably the biggest culprit in mold and mildew problems.

Mold spores are found everywhere, and can grow on any organic surface, given the right conditions. To prevent mold growth, keep all surfaces clean and dry, and provide plenty of ventilation.

Solutions

Food - Remove the food source. Most IKEA furniture uses the backboard as an important part of the framing. Removing the backboard could cause the shelving to collapse, so be sure to either clean and treat the backboard or replace it with a new backboard from IKEA. You can also get wood panel sheets from home improvement stores and cut it down to fit.
Warmth - You might look at moving your furniture around to see if a different location is better. A key to reducing warmth is improving air circulation.
Oxygen - Sealing the backboard will prevent oxygen and moisture from being accessible to the backboard.
Water - Reducing your home's humidity is the right solution. Invest in a low cost humidity sensor and monitor your progress in keeping humidity in the 30-50% range. Look at your home's fan system in the bathrooms and kitchen to make sure you are venting steam from showers and cooking to the outside instead of letting it build up in your home. You can call an HVAC specialist to verify your home's ventilation system is working correctly. If you have condensation on your windows it is a sure sign you have too much moisture buildup. If you have a fish tank or other open sources of water you may want to look at keeping IKEA furniture out of that room or putting a cover on the water source.

Step 5: Call to Action for IKEA

This is a problem I wish Ikea would address by doing a better job of sealing both sides of the backboard and to stop using paper based tape and glue material.

These unsealed wood based tape and backboards soak in moisture and provide food for mold and mildew. If IKEA would simply laminate both sides of the backboard it would solve this problem and give an added benefit of giving consumers two design options to choose from.

I can understand IKEA wants environmentally sustainable and recyclable furniture, but consumer concerns over human respiratory issues regarding the toxicity of mold is something that should come from IKEA or if needed by governmental consumer safety agencies requiring them to seal the backboards on their furniture.

If IKEA wanted an environmentally sound solution they could use a thin layer of wax to keep out the air and moisture.

Until then I would encourage folks to do the following:

Regularly check the backsides of IKEA furniture and the undersides of drawers.
Publicly share photos of Ikea furniture with mold and mildew with the hashtag #MoldIKEA
Ask Ikea for free replacement backboards by reporting the problem as a product defect

Hope this is helpful, and someday soon unneeded!