Do you need a box spring with a memory foam mattress?
A memory foam mattress needs to be on a firm, supportive surface. Typically, people have a box springs or foundation that they use with their current bed, and wonder if they can use they can use this existing piece with their new memory foam mattress.
(A foundation looks like a box spring on the outside, but it doesn't have coiled springs on the inside and instead is built to be very firm and feels almost as firm as a platform. Most beds these days tend to come with a foundation rather than traditional coiled box springs.)
And I've found that as long as the box spring or foundation is firm and supportive, and doesn't have much give, these can work well with a memory foam mattress.
As can a slatted bed or slatted platform, as long as the slats are sufficient to support the bed. Typically this means slats of a few inches in width and an inch or two apart.
A solid decked platform, though, can cause problems because these may not allow sufficient ventilation to allow the mattress to breath. This is important because as you sleep, your body puts out a lot of moisture and this will pool at the bottom of the mattress if the mattress doesn't have good airflow. Over time, this can cause mold on the bottom of the mattress, so if you want to go with a solid wooden deck you might want to drill a fair amount of holes in the bottom to allow good air flow. If the deck is plastic, I would recommend looking at other options since I don't think a solid plastic deck really will work with a memory foam bed.
I've also been asked if you can use a memory foam mattress on the floor, and this isn't a good idea because of this lack of ventilation issue. I have used a foam mattress on the floor over the years, and I learned early on after having mold issues that if you are going to use a foam mattress on the floor, it is important to tip it up on its side every day or two to allow the moisture to dissipate in order to avoid having moisture form on the bottom that can lead to these sorts of problems.
Lastly I've had customers ask me about the wire framed platform options they've seen that offer good storage below the bed. These say they are ok to use with memory foam, but I don't believe that they really are good options since the wire frame itself doesn't provide a firm, supportive base for the memory foam to sit on -- and this will cause the memory foam to feel much softer than intended. And I also am concerned that over time the wire itself will cut into the memory foam and end up ruining the bed.