Be aware of the bad chemical odor your new mattress will probably have. It takes several days to several weeks for this smell to go away. Some people cannot fall asleep with the bad odor and need to let the mattress air out for a couple of days before using it. NASA actually developed memory foam, but the astronauts did not want to use it because the pads would not air out in the small, airless space ship.
Memory foam can be flammable because is made from polyurethane. However, laws require memory foam to be flame resistant. Because this product is synthetic and uses chemicals in its production, some people are averse to sleeping on it. They prefer organic bedding.
Some people think memory foam mattresses are too expensive. However, if you go with the cheaper versions, you will not have as good a product. The cheaper versions may be hotter, for example, because they are less likely to have breathable foam, which will be more comfortable for you.
You may have a harder time turning over in bed or getting out of bed with a memory foam mattress. Because the mattress conforms to your body, you will not have the springiness that you are used to with a regular mattress.
Watch the sizing. The cheaper mattress pads may not be true to size and may not fit properly on your mattress.
Make sure you are not putting a new memory foam topper on an old, saggy mattress. In order for the memory foam to work properly and conform to your body, you need to put it on a decent mattress. If you mattress is old, get a new one, and your memory foam should work fine.
If you have back problems, memory foam may not be the right type of bedding for you. It works for some types of back pain, but not others.