No. You cannot kill someone just because he enters your house uninvited.
You have a right to self defence. If you are attacked you can fight back. Theoretically if you kill someone while defending yourself you will not be convicted. But in reality... a different story.
Meet this guy:
His name is Ivan Sinanović, and he is (was?) a priest. And a biker. And while he was a priest he supported one poor family with half of his salary.
In 2012. he was a parish priest in a small village in Croatia. The president of the village council did not like the priest, because the priest was planning to expand the old cemetary near the church and to offer burrial places at 1/3 of the price that the village council was charging at the "official" cemetary. The president of the village council was probably making some illegal side-money from the cemetary business.
After a night of heavy drinking, during which he claimed multiple times that he will take care of the priest once and for ever, the president of the village council who was "aggressive when drunk", as witnessed by one of his friends, went to the priest's house, broke the door with his leg, started shouting that he will kill the priest, and when the priest arrived, started violently hitting the priest. If I remember correctly, at the time, the priest's sister and nephew (niece?) were also staying with him in the house. So the priest started defending himself from the drunk, agressive guy, who broke into his house at the middle of the night. Being stronger and sober, he managed to throw the attacher to the ground. While falling down, the attacker hit his head bad, and died.
So, did the police/court acquit the priest from all charges and thank him for taking care of an aggressive guy? Nope. They sentenced him to 4.5 years.
So, if someone drunk breaks into your house in Croatia at the middle of the night, and starts hitting you and yelling that he will kill you, and you have a child in your house, be aware that you can get 4.5 years in prison if you defend yourself.
The simplest answer is a flat-out "no". This is not legal anywhere -- at least not the way you worded it. Even in jurisdictions that are permissive of defending one's property and of preemptive force (most notably parts of the USA), it's not open-season on trespassers. This isn't the Walking Dead.
If an old lady with dementia wandered into your house and swooned about, threatening to smash your china into smithereens or pee on your rug, shooting her would be a crime, even in Texas. So let's be reasonable and add a few necessary clauses: reasonable belief of trespasser's malicious intent, and reasonable belief that deadly force was necessary to prevent it from coming to fruition. This matters even in Texas.
Okay, now that the setup makes sense, here is the deal with Croatia: it is only legal to kill an intruder if they attack you (fuck upholstery, they may shred it to bits before your eyes, provided you are unsuccessful at shooing them away with a stick or hitting them on the head with a frying pan, et caetera), preferably if they have a gun, otherwise you might be charged with voluntary manslaughter or even second-degree murder (note: we have a different classification of homicide). In general, you are allowed to defend yourself with equal force or less. If you shoot someone who's unarmed and isn't violating you or beating you into a pulp, Croatian law sees you as taking things too far. There are cases where a home-invasion victim (note: we don't have such a dramatic term for it, aside from "breaking in") was charged for killing the intruder (see Nikša Orlić's answer). There are cases where wounding the intruder is also a crime -- a murder attempt. Killing people is not taken lightly. You're better off trying to avoid it.
The thing is, finding a stranger or two in your backyard (even your home in some cases) is not as strange and dangerous an occurrence in Croatia as it is in the USA. Personal property isn't as strewn with metaphorical landmines (we do have some literal landmines left over from the war, so be warned), and strangers aren't as armed with potential guns. Furthermore, we have a small but notable population of military veterans with PTSD, and generally unhinged people who have been through a lot of shit and who may go on some kind of weird rampage out of despair. Many people empathize or are at least used to dealing with them.
The murder rate is 3.5 times less than in the USA, so we must be doing something right. On that note, it probably wouldn't work as well in such a large, heterogenous and dispersed society as the US. It really is culture-dependent on a deeper level than laws can control.
