Q:

Is there any pan in which water or liquid shouldn't be boiled?

1. Should anything be boiled in aluminium pans? In general, are there any pans that boiling will damage? 
2. What kind of pan is this? I don't know because I no longer have the receipt. Has the pan abraded or eroded?  Please see the pictures below (click for full size)

A:

A picture would help also!
If your pan has a non-stick coating that is flaking off... I'd recommend to discard it.  The non-stickness is compromised and the non-stick stuff is probably not good to eat. That said, in my experience non-stick coatings are sensitive to scratching from utensils... not so much from the food itself. It certainly depends on the non-stick material: e.g., PTFE, enamel, ... 
Sounds like you're mostly interested in your aluminium pan, but also for posterity...
Cast iron requires some ongoing care and feeding.  Boiling or cooking certain things in certain ways can cause cast iron pans to lose seasoning.  For example, acidic foods or very wet things without fat will tend to degrade the seasoning, leaving you with a pan that's less seasoned and perhaps with some of the "seasoning" and/or metallic taste transferred to your food; it might not taste as good, and future cooked food will tend to stick more.  For example from Lodge, recommendations for foods not to cook in cast iron.

EDIT:
We've come a long distance from the literal meaning of your question.  I'll focus on your comment and picture.
It looks like your pan is aluminum, coated with PTFE (brand name "Teflon®") or some similar substance. If I'm correct, your pan is probably very light and heats quickly.  It also looks like the pan/coating is badly scratched, and perhaps the coating is peeling off.  This means that you're eating small bits of plastic, and the non-stick nature of the pan won't work as well.  If it were mine, I'd discard it and never buy anything like it ever again. :)  There are plenty of products out there that have more resilient non-stick properties, from well-seasoned cast iron to manufactured coatings.
MORE:  

As to safety and uses, DuPontTM itself gives answers to some questions about its brand. That says that boiling (e.g., water) in nonstick is not harmful. So, it sounds like you can boil things in it. That said, PTFE is actually a rather good thermal insulator (~500x worse than aluminium, for example). This seems undesirable for boiling something, when bulk heat transfer is what you seek. It may not make much difference because the coating is so thin, but low thermal diffusion suggests to me that boiling water in a bare metal pan will be more efficient, though a quick search doesn’t seem to be conclusive. Not my choice, but YMMV.
There are many recommendations of what not to do with your non-stick pan, such as this one. Depending on what you’re boiling there may be a recommendation against it.

