Well for starters, he coined the term 'robotics'.
EDIT: I would also add that the Three Laws have certainly sparked endless amounts of discussion in the field of robotics as relates to ethics.
I would say that Asimov is the first to document the challenges and pitfalls of debugging a system (especially with regards to black-box testing), and the illusion of malicious compliance that programs (robotic or computing) seem to take pleasure in.
I often think of SPD (Speedy) when trying to fathom a particularly bizarre pattern of behaviour.
Robots in SF that predated Asimov were mostly characterized in a Frankenstein or Golem fashion; destroying the robot would save the day and conclude the story. He thus pioneered tolerance for non-human and non-organic intelligence.
By presenting intelligent, human-like robots, he advanced the field of thought as to what a robot is, how it relates to humans and its own human nature, and what role AI has to play in humanity.
I believe his contribution is very much similar to that of Roddenberry or any other successful sci-fi creator:
He inspired people to become scientists, to help build the future that only previously existed in fiction.
As mentioned above, he did coin the term "robotics."
Asimov coined the term "robotics" in his 1941 story "Liar!", though he later remarked that he believed then that he was merely using an existing word, as he stated in Gold ("The Robot Chronicles")
However, that appears to be about it. In that same essay in Gold, Asimov writes (page 167-168 in my (first, 1995) edition of Gold)
I myself have never actually worked with robots, never even as much as seen one, but I have never stopped thinking about them.
But, he contributed to the field of robotics in other ways:
Joseph F. Engelberger, studying at Columbia University in the 1950s, came across I, Robot and was sufficiently attracted by what he read to determine that he was going to devote his life to robots.
I have met other roboticists such as Marvin Minsky and Shimon Y. Nof, who also admitted, cheerfully, the value of their early reading of my robot stories.
(same essay, page 167)
The essay (according to the book) was copyrighted in 1990, two years before his death in 1992, so it's doubtful that he started studying with robots at that late point.
Big dog, DARPA cars, partial humaniform bots from the east, endless forms of miniaturization — they all have traces of Asimov.
But the kind Asimov had in mind? I don't think this question can be answered fully at present. For instance we have not even arrived at the point where any of the three laws of robotics are even relevant.
Try running a search on Google Scholar for "three laws of robotics" and see what comes up. While none of the actual tech (or, to be precise, techno-babble) that Asimov used is actually in evidence today ("Positronic brain" was coined as a play on "electronic", as positron <-> electron), the basic concepts are still brought up whenever people discuss autonomous systems and their responsibility towards their operators and bystanders.