When installed correctly, a dishwasher shouldn’t move at all. If it is freestanding, you should be able to move it to a new location, but when you move it, it should only move horizontally. Built-in dishwashers, however, will move no direction.
Yet, if you have found that your dishwasher tilts forward, it needs to be addressed. Contrary to popular belief, the waterproof seal on a dishwasher is not waterproof. The seal is meant to prevent water from leaking when splashed against the door during the wash process, but when a dishwasher is tipped forward, that water will start to leak out. Furthermore, when a dishwasher is tilted, it can interfere with its ability to wash dishes and needs to be addressed.
If your dishwasher is tilting forward, what you need to check depends on your model. On freestanding models, you will need to check the legs. These can sometimes come out of level or break, in which they will need to be replaced or readjusted. On built-in models, you will want to check the mounting brackets. These secure the dishwasher to its alcove, and when they come loose, the appliance will tilt.
If you have noticed that it is not your whole dishwasher that is leaning forward, but rather the open door itself, then the cause is pretty easy to determine. That is most definitely a hinge problem. When this is the case, you can replace the hinges, but it may require some extensive disassembly on the door and the appliance in order to remove and replace the hinges.
Regardless of which problem is causing your dishwasher to tilt forward, or at least appear to be tilting forward, the solutions are generally pretty simple. In most cases, it is a leg that needs adjusting or mounting brackets that need to be tightened.