Is there any standard size in Custom PCB Manufacturing?
Sometimes PCB makers have a per-panel price. They will tell you the size they are using..or more importantly, what area you have to work with-- usually usable area (not panel size) is at least 10" x 16", maybe up to 10.5" x 16.5" or a bit more. That would be a small panel. For large production I believe larger panels are more typical. Typically phenolic single sided boards use much larger panel sizes. This reference lists typical standard PCB panel sizes as follows: 



Panel borders (maybe 0.5" on each side) take away from that area. 

It is not particularly important unless your PCBs (or your self-panelized PCBs) are getting up to the size where you only get a few from a panel- materials are not really the biggest part of the PCB cost in prototype volumes despite you being charged per square cm or inch. If your PCB or panel is approaching or exceeding about a letter-size or A4 sheet and your quantities are more than hundreds (of that size, it could be thousands of panelized boards) it might be worth worrying about. 

When you order loose boards you don't have to pay for router kerf and tooling strips either as PCB area (well, you do but it's not figured directly into the costs) or as shipping mass, but extra costs are incurred later. 

It might be interesting to play with the online calculators that many PCB makers have and see if panelization figures into their calculations. You would expect the cost per square inch to not follow a straight line as the size gets bigger. Keep in mind though that getting large defect-free areas gets more expensive as the area increases so a large panel (without X-outs permitted) may be more expensive per square inch than a smaller panel. It may not be important if the technology level is low, but for multilayer boards with fine pitch and tiny holes it is not negligible. Often the online quotes are not the final quote in such cases, and they will come back with an adjusted quote (hint: it is never lower).