For example if two citizens from same country travel to Asian countries like Malaysia and Thailand, and one of them robs the other citizen while in Asia, is it worth reporting it back in Europe? Or there is no chance that Europe police will solve the "crime" in Asia?
Crimes should be reported where they occur. With the exception of very major crimes, countries will generally not enforce the laws of other countries, although in certain cases they will agree to extradite their residents or citizens abroad if they have committed crimes elsewhere.
This even applies with subnational boundaries. For example, if you get robbed in Toronto, reporting it in Montreal won't be all that effective since each city has its own police department, and the laws vary somewhat between Canadian provinces.
It depends on the crime and on the European nation - the EU does not have a single judicial jurisdiction yet, those powers still reside with individual nations, and thus the situation is the same for EU as it is for non-EU nations.
France for example considers any felony and some misdemeanors* committed by, or against, its citizens to be within its own courts general jurisdiction, regardless of where the crime was committed.
Many other EU countries either consider extraterritorial jurisdiction to be within its own general jurisdiction or in specific jurisdiction for certain crimes (for example, travelling abroad to commit child sexual abuse etc).
* The French word "crime" mentioned in the law means "felony", not "crime" (which can mean any kind of offense, from pickpocketing to first degree murder). The French word "délit" roughly means "misdemeanor", which is a serious offense but not as serious as a felony.
There is no such thing as "Europe Law". Europe is not a country nor a jurisdiction, it is a continent.
That being said, any court can decide to take any case for any reason. Usually, there are laws and/or rules which state which crimes a court is responsible for. There is no limit to that. For example, there is a law in Belgium that says that Belgian courts have jurisdiction over certain particularly egregious crimes (crimes against humanity and war crimes) regardless of where they occur, who was the perpetrator, and who was the victim. There doesn't have to be any relationship whatsoever to Belgium. Whether or not someone who was tried in a Belgian court for something which has nothing to do with Belgium actually accepts the ruling is another matter altogether. As long as you don't travel to Belgium, nothing is going to happen to you.
Now, if a Belgian court decides to try, say, George Bush or Donald Rumsfeld for war crimes committed in Iraq, and even if they sentence him to prison time, whether they can actually make him appear in court and get him to go to prison is a totally different matter. The US are not going to extradite them. (In fact, the US pressured Belgium into amending the law so that this couldn't happen, because there were actually people who asked the Belgian courts to prosecute Donald Rumsfeld.)
It all depends on the country.
Generally, it's not worth reporting the crime in Europe, in most cases. That is for two reasons.
First, penalties in Asia are much, much more severe (you definitively do not want to get in trouble with the law in Malaysia!), and while police will probably not bother investigating petty crimes, if the crime is anything substantial, they certainly will, and both treatment of the suspect by the police as well as punishment will be... let's say, harsh by our standards. No additional punishment needed, really.
Second, while it is true that some EU states (France, as an example) in principle consider their law applicable to all their citizens even abroad, this is mostly a theoretical thing which is hardly worth the paper it's written on. For most crimes, at least. Police isn't going to do anything for most crimes.
Other EU states (Germany, as an example) explicitly state early in their penal code that the law applies within their national terriorty including ships and airplanes which have the right to display their banner, followed by some exceptions in the "small print" that state which crimes are also persecuted abroad.
Those exceptions are high treason and terrorism, crimes against humanity or life (read as: torture, murder, trafficing, forced prostitution, trading organs, etc), kidnapping, and crimes involving serious bodily harm, bribing officials and delegates, counterfeiting, piracy (in terms of capturing ships, not software!), shooting at airplanes, sabotaging nuclear plants, that kind of thing.
So... unless you are really one tough bastard of a supervillain, this doesn't apply to your usual everyday crime.
You can, however, provided you have sufficient evidence to avoid risking a sentence for false accusation, do it nevertheless. It costs you nothing, and it remains in the records. Everything and anything you report remains in the records forever.
It has no legal consequence whatsoever, except when the next thing happens maybe in 5 or 6 years, possibly to someone else, the policeman looking up the name will raise an eyebrow (I've just had this happen last week). Which may make the difference between the policeman judging your situation as "plausible" or "not plausible".