I believe there has to be some grouping of values.
For example lets say your items are objects in a room. Then different types of objects have different attributes. For example books have publication date and number of pages, chairs have color pattern and height, etc.
In this example, you make an item table, a book table and a chair table.
You could make an "additional values" table that holds generic information as above, but what you really want to do is figure out the "types" of the different groups of attributes and then make every one of those types it's own table.
Is there a set of values that all items have? There has to be at least one which is a type field (this describes where the other information is stored. I expect every item will also have a name and a description. This is the information to go in the item table.
Then you make additional tables for the different types itembook, itemchair etc. There may even be some overlap. For example itembook, itemhardback, itempaperback would be 3 tables used to describe books.
I believe this is the best solution to your problem. It will still allow you to extend, but it does put a framework around your data.
Of course there are systems that do it the way you describe, but unless you are building a tool that others are going to reuse for many different projects, it makes sense to design the system for the task at hand. You end up falling into the over designing trap otherwise. (IMHO)
On the other hand, if you are going to go the totally generic direction I suggest you use one of the systems that already exist that work in this way (entity framework, app framework, etc) Use someone else's don't start from scratch.