Well project Icarus aims to send robots to a nearby star, for a flyby, up to 15 light years away at up to 15% of the speed of light, so that they take at most 100 years to get there, and for closer stars more quickly, depending on their distance.. Page on arxiv.org That's with future technology, we can't do it right now.
If we could send probes at that speed to Kepler 438b, it would take 3,133 years for them to get there. So I imagine we are likely to try nearer targets first :).
There are ideas to send mini robots at close to the speed of light, as well. If they are tiny perhaps you can send thousands, even millions of them, and only a few get through. But that's based on the idea of self replicating nanobots, so that they can build bigger structures when they get to the destination system, to explore it and "phone back", it's rather beyond what we can do at present.
When you get closer to the speed of light, then the interstellar hydrogen atoms are a significant radiation hazard for your bots, needing a fair bit of shielding. Because they become protons hitting your spaceship at close to the speed of light. This paper suggests a limit of about 50% of the speed of light unless you have massive shielding. Conferences, Proceedings, Journals, Open Access Journals, SCIRP.