You would be hard pressed to find a dental clinic that would give you amalgam fillings, as the production and use of mercury has been outlawed by the Minamata convention. Newer fillings are going to be composite resin fillings that are made of several different kinds of synthetic materials, including Bis-GMA, glass ionomer and other monomers that form an artificial resin. This synthetic material is photosensitive and hardens when a light is shined on it, filling in the recess or cavity it is placed in perfectly.
But what of fillings that are already in the mouth done years ago? Amalgam fillings are usually replaced for a number of reasons, the primary one being aesthetic. The black spots make it very easy to identify amalgam fillings and they are visible even from a distance, as they are such a different colour than living teeth. The other reason is because amalgam leaches heavy metals into the bloodstream if left in for long enough. As all materials, amalgam also degrades over time, meaning it starts to fall apart. Amalgam fillings are an amalgamation of tin, silver, mercury and a whole bunch of other materials, almost all of them harmful to the human body. Mercury in particular is very bad for your central nervous system. If you needed another reason, they also make inferior filling materials to composite resin for one reason alone: they shrink over time. This means that the cavity will be exposed, and infections and further tooth decay often start from around old amalgam fillings. Composite fillings, on the other hand, are primarily adhesives, and will stick jot the inside of the teeth, and will not shrink over time, as they do not dehydrate and do not interact with water at all.
When you go to the dentist and tell them you want your amalgam fillings replaced, they will more than likely comply with you and suggest getting composite resin fillings. Getting the amalgam removed is a good idea, because it will tax your system less, and the tooth will be safer, as further decay is unlikely, and it will be more aesthetically pleasing. The procedure does not take significantly longer than getting a tooth filling, and shuls be over in half an hour to 45 minutes or so.