Tables should not be used on web sites for several reasons- the most important reason being accessibility. A screen reader would have to read through the entire table one cell at a time. Even in the best case, this would still be cumbersome for the user. The other major reason is tables are not responsive (viewable on a wide range of devices and screen sizes). No matter how well designed, a table that looks good on large screens may not be usable on smaller screens.
When confronted with tabular data you need to ask yourself about the nature of the data and how the user should consume the information. In most cases, using Alternative Solutions to Tables is the best route.