All the assumptions you made are quite true in all the aspects. JARVIS stands for Just A Rather Very Intelligent System in the movie. So what can Jarvis do? In the movie we saw him as a computer which acts as a Digital Assistant. Jarvis handles each and everything about Tony Stark including his work, writing programs for his suit, handling security of his house and all.Technically we have not yet reached that far yet. But

apart from Film, is it possible to have such intelligent computer in the real life ?

and Researchers say:

Well Answer is Yes cause i believe impossible itself says i am possible.

If we view this problem from programmers point of view

apart from the customization one important thing is the accurate voice recognition system and yes this is not a General voice recognition system that has a simple database of pre-described commands and compare the human voice to the commands stored. Jarvis Computer is like a Responsive voice recognition system that can even raise questions by itself and wait for the answer. I hope you can understand what I am talking about. Yes we need to Put some Artificial Intelligence Programs to avail such feature which is not easy.

But some geeks have started working on it. Like Chad Barraford who has already made device named DIY which can work almost like Jarvis. It can:

Jarvis Can Talk Barraford developed a language interpretation system that employs MacSpeech Dictate, a program that converts speech into text so Jarvis can interpret it. In this video, Barraford demonstrates Jarvis's listening and speaking abilities.

He Can Wake You Here, Barraford demonstrates Jarvis's alarm clock system and daily weather report.

Jarvis Watches Over the Home Barraford gave his dog and his close friends RFID key chains so that Jarvis would know when they are in the apartment. "He figures out who is home and who isn't, and he changes the environmental settings based on that information," Barraford says. For example, Jarvis uses the X10 system to turn off the lights if no one is home, and when friends are over he keeps Barraford's Facebook notifications private, instead of reading them aloud like usual. In this video, Barraford demonstrates the RFID tag reader.

And He Can Even Help With Migraines Jarvis really comes in handy when Barraford gets a debilitating migraine headache, which occurs about once every other month. An instant message is all it takes to switch Jarvis into migraine mode, which calls for him to send an e-mail to Barraford's boss, update Twitter and Facebook and dim the apartment lights.

For all these functions The complete pack of Jarvis includes

Mac Mini
radio-frequency-identification (RFID) tag reader
X10 home automation system
wall speakers and a wireless microphone.

So we cannot say we have made an exact thing like Jarvis, but we can surely say that we are approaching to create like one slowly.

Having worked on AI, the correct answer is

No, no such system exists and might only exist in decades.

While I agree with other answers that you can emulate JARVIS to some degree and have him follow simple pre-programmed commands, that is VERY different from what JARVIS actually does.

Let's start from the beginning. The current top answer lists JARVIS's capabilities as such

• Jarvis Can Talk
• He Can Wake You Up
• Jarvis Watches Over the Home
• He Can Even Help With Migraines

All of this is simple (not really, but simpler than what I will describe later) to program into an AI agent.

Speaking

Voice recognition and synthesizers are becoming increasingly more common (just look at Siri and Google Voice). They work by listening to audio, filtering noise, and converting speech to text. Then, they use text analysis (like MALT) to extract dependencies in the text, they compare them with hundreds of pre-built commands and match them accordingly. They execute whatever task was chosen by the user (tasks which were pre-programmed) and reply, using speech-to-text software (which is the oldest of these technologies! Today you can listen to Google Translate).

Alarm

Ok, this is stupidly simple. You pick any calendar out there (Microsoft or Google or whatever), or any sort of alarm system (even from your phone!) and it can do this. It's a standard technology in any smartphone nowadays.

Security

This is more complex technology, and not so readily available. Smart houses are becoming a thing (Bosch is investing a lot in this area, for example), and they have the sort of capabilities you described. They monitor who is in the house, temperature and lights, locks, even food in the fridge. Again, these are mostly pre-programmed tasks that the system eventually learns to use at the appropriate times with machine learning techniques.

Health

There are also systems that track health status and the likes. For example, some smartwatches are tracking your heart rate and it's not a big leap to assume they could be configured to emit some sort of alarm when the heart rate had a sudden change.

That being said, JARVIS does something quite apart from this.

JARVIS is capable of reasoning. Real, actual, reasoning. He can have a conversation with you, inquire new information, associate, filter, discard, and compute conclusions. I cannot emphasize how this is revolutionary. From all the stuff Tony Stark invented in his comics, a Artificial General Intelligence (AGI) such as JARVIS is the most impressive.

Research today is just grasping how reasoning can be learned by a machine. It's something that has always been programmed by humans, not something a machine has ever learned from simple analysis of data, like we humans do. Machines can learn information from data, like, show them pictures of cats and dogs, and after a while the machine can distinguish between them. But if you show them a bunch of different sized spheres in a box and ask "which sphere is the farthest away from the largest sphere", then this is something immensely hard to learn.

Google DeepMind (the leading research group in Neural-based AI) has published in the last few months 2 articles where reasoning is being learned by the machine. Check them out here and here. If you read through them, you'll see how groundbreaking the research is, and how there's not much similar to that. An AGI such as JARVIS is amazingly more developed that these efforts, and it will still take years until we can reach that level of autonomy, efficiency, and general intelligence.

Just to provide some more links (I'm not gonna try and match the other answer):

Jarvis is shown to interact in conversation. This involves voice recognition and interpretation. Voice recognition is the conversion of sound to text/language and is actually easier than the interpretation part in which the AI has to really understand what you're saying. Siri is indeed an example but still rather simple as it mostly uses the same basic set of commands/answers. Others include cleverbot and jabberwacky. Most of them use machine learning underneath to interpret previous answers. At the moment, most of them are not that human-like but still fun to try.

A lot of AI development is also being done in the gaming industry to create human-like players. Read this article on gaming AI and the Turing test.

Well, Mark Zucker, the CEO of facebook have worked on the same concept as that of J.A.R.V.I.S and is even ready with a prototype.

https://www.facebook.com/notes/mark-zuckerberg/building-jarvis/10154361492931634/

It connects various components of household, turns lights off/on, checks the door for guests(faces to see who has come), plays music on the rooms, chats using the messenger bot, etc.

More information here: business insider.

I don't believe any such system exists, in the same way that no real Iron Man suit exists. JARVIS is mentioned many times in the comics I believe and so was just a character to be carried across (just like Stark and Pepper).

I'd suggest that the largest available similar system is Google Voice or Siri!