Question: What is the difference between *to allege* and *to claim*? Can I use them interchangeably? Or perhaps I can only *allege* something illegal?

For example, from CNET:

> 
> Over the past several months, the two companies have been embroiled in
>  litigation in which Apple **alleges** that Samsung illegally copied
>  technology and design aspects of the iPad to create the Galaxy Tab.
> 
> 
> 

If I replace *alleges* with *claims*, does it change the meaning at all?

Answer: 
To *allege* is always to accuse a party (human or corporate) of wrongdoing. You may, however, *claim* something without the accusation of wrongdoing.

For example:

* You can *claim* that a new product is far superior to its competitors
* You can *claim* that a storm damaged your conservatory by blowing your neighbour's tree down so that it fell on the conservatory
* You can *claim* that the dog ate your homework

In none of these situations are you accusing anyone of anything (except, possibly, the dog. But he isn't a legally responsible entity and you aren't asking your teacher to take action against him).

You can *claim* that someone is guilty of wrongdoing against you but this can be less aggressive that *accusing* them of it. For example:

* You can *claim* that a rival's product breaches a patent you hold in some significant detail.
* You can *claim* that a neighbour's tree is damaging your conservatory because the branches are scratching the glass and wearing away the frame
* You can *claim* that your sister spilt coffee over your homework

If you *claim* negligence or deliberate wrongdoing on the part of another this is the same as *alleging* it:

* You can *claim* or *allege* that a rival has copied your patented product deliberately.
* You can *claim* or *allege* that your neighbour has cut down his tree so carelessly or incompetently that it has fallen on your conservatory
* You can *claim* or *allege* that the class bully has thrown your homework into the river.

There is an overlap in the meaning but *allege* is stronger, more associated with criminality and tends to imply a higher standard of proof. *Claim* is wider in application, slightly gentler and somewhat less formal in its implications.
The only difference is one of diction. "Alleges" is in a much higher register than "claims." "Alleges" is also preferred in legal contexts.