Practically any database should be able to run such queries.
In the case of SQL, using a simple WHERE ... LIKE ... condition with wildcards should be sufficient for simple cases.
The interesting question will be how to scale this once you are dealing with much larger amounts of data, think YouTube for video portals. But until performance really becomes an issue, adding additional complexity can most likely be considered premature optimization and should be avoided.
solved Which DB technology is sued to solve the following search issue? [closed]