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.
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).
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.
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.
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.