Practically speaking 2" (50mm)  or 3" (75mm) thick steel is about the limit for an abrasive waterjet. In same specific cases even thicker.

If you want to cut steel that is thicker than 3" (75mm), then you need to ask how long can you afford to wait for your part to be finished?  The thicker the material, the longer the wait, and you just have to ask yourself if it is cost effective.  Sometimes it is, but usually it is not.  In the case of exotic materials where the material is extremely expensive and difficult to cut by other means, then 3" (75mm) and thicker may be practical.  Titanium is an example of such a material.

If the cut is along a straight line, or a shallow curve, then it is also more practical to cut thick.  However, if there are sharp corners or curves, then the cutting very quickly becomes extremely slow.

For soft materials, we can cut extremely thick.  For example, we could cut 2 foot (600mm) sponge pretty easy.  For hard material, like metal, once we pass about 2" (50mm) thick, we may have to think about whether or not you are going to work on your project. 

However, this is not the norm.  The aluminum piece is pretty simple, but it may take 24 some hours to cut.