Today's electronic digital computers are often referred to as universal Turing machines. That is, the concept of the UTM is used to understand today's stored-program electronic digital computers. But is this concept adequate? In fact can today's computers do things that UTM's can't do? If they can do more than a UTM can do, it could be important to AI, since AI (and Searle and his Chinese room argument) use the UTM concept to define the abilities of AI's research and development platform - the electronic digital computer.
Short answer is no; modern computers cannot do things that Turing machines can't do. What they can do is run very sophisticated, complex Turing machines that simulate things that Turing machines would not be able to do.
This is an important point; Artificial Neural Networks, Genetic Algorithms, Fuzzy Logic Algorithms, and all the other types of 'machine learning' and 'artificial intelligence' mechanisms that computers can execute are still deterministic and algorithmic in nature. They still run a strict series of commands, and most importantly do not deviate from those commands no matter what. They're good at solving NP (Non-Polynomial) problems only insofar as they emulate the process that a human would undertake, but that emulation isn't perfect and may never be. Even the 'random' elements in a Genetic Algorithm isn't truly random; you seed an ordered (but seemingly random) list of numbers with a starting value and every call for a random number is taken from this list from a point determined by the seed value.
In that sense, computers can accumulate new data and can use that data to drive their behaviour, but only according to the rules of a Turing machine. In that sense, the computer cannot extend itself beyond its programming, even though it may seemingly emulate that capacity by the way it uses the data it accumulates.
There is some debate going on now as to whether or not a quantum computer will break that model, but then if it does, then it's not a 'classical computer' and we will have only used the name 'computer' for it to extend a metaphor that we already understand. That said, whether or not a quantum computer can operate in a non-deterministic way will be a very interesting question to try and answer in due course.