Coffeemakers, especially the basic ones with glass carafes, have few moving parts and can last for years. But, most coffeemakers are used on a daily basis and eventually stop working as well as they did when they were new. When this happens the decision must be made to either repair or replace the machine.
Replacement Carafe
Coffee Makers Single Cup
If you have a coffeemaker with a glass coffee carafe, this is by far the most common part to "wear out", usually by breaking into hundreds of pieces. Fortunately, all the major companies make replacement carafes. These are usually readily available and cost far less than an entire new coffeemaker. Sometimes a glass carafe can be replaced by a thermal carafe, but this is uncommon. Thermal carafes have more complex mechanisms, especially on the lid. Although they aren't as easy to break as glass carafes, the lid mechanism can be damaged. You can usually find replacement thermal coffee carafes at the same merchants that sell replacement glass carafes.
Mineral Build Up
If the water isn't flowing through your coffeemaker you most likely have a buildup of calcium and other minerals. This is very common in areas that have "hard" water. Fortunately, this can usually be fixed both easily and inexpensively. Prepare a solution that is 50% vinegar and 50% water, enough for a normal pot of coffee. Vinegar is a mild acid and will dissolve the mineral buildup in your machine. It is also completely harmless - Don't use chlorine based cleaning products (chlorine is quite poisonous)! Run the vinegar solution through your coffeemaker and it should remove the mineral deposits. If the deposits are heavy, you may need to run several batches of vinegar-water solution through the machine. Most of the time this will take care of the problem, but occasionally the buildup is so thick that it completely blocks the flow of water through the coffeemaker. At this point you may need to replace your machine.
Broken Heating Element
If the heating element of your coffeemaker stops working, it's nearly always easier (and usually less expensive) to replace the entire machine. Most companies do not make replacement parts for their coffeemakers (except for replacement carafes). The only exceptions are the very expensive top of the line machines that cost hundreds of dollars.
If the heating element of your fifty dollar coffee maker stops working, it's definitely time to replace it.