Any good recommendations would require a much better understanding of your requirements, but here are some comments on the options you mentioned, as well as some additional thoughts.
1) Entity-Attribute-Value (EAV) Design: This is the option you describe where you have a table that has columns for ColumnName, Type and Value. This option has the advantage of being able to accomodate unlimited new columns easily, but I have found it to be painful when the time comes to retrieve meaningful data back. For example, say you have rows in this EAV table for {Color, varchar}{Red, Green, Blue}, and {Size, varchar}{Small, Medium, Large}. If you want to find all the small green items, you need something like this (untested SQL of course):
SELECT *
FROM ITEMS
WHERE ITEMID IN (SELECT ITEMID
FROM ITEM_ATTRIBUTES ATT INNER JOIN ITEM_VALUES VLS
ON ATT.AttributeID = VLS.AttributeID
WHERE ATT.ColumnName = 'Color' AND VLS.Value = 'Green')
AND ITEMID IN (SELECT ITEMID
FROM ITEM_ATTRIBUTES ATT INNER JOIN ITEM_VALUES VLS
ON ATT.AttributeID = VLS.AttributeID
WHERE ATT.ColumnName = 'Size' AND VLS.Value = 'Small')
Contrast this with having actual columns on the items table for color and size:
SELECT *
FROM ITEMS
WHERE COLOR = 'Green' AND SIZE = 'Small'
In addition, you will have a difficult time maintaining data integrity, if that is important for this app (and it is almost always important, even when you are told otherwise). In the example above, you will need to implement extra logic if "Color" should be limited to Blue, Green, and Red. Also, you will need to implement even more logic if certain colors only come in certain sizes (example - blue items are only available in small and medium)
2) User-Defined Columns: Just giving the user the ability to add additional columns to the table has the advantage of making data retrieval simpler, but all the data integrity issues remain. Also, your app usually requires extra logic to deal with the unknown columns.
3) Pre-Existing Custom Columns: I have worked with a few apps, such as CRMs, that provide a dozen or more columns already in place for user definition. Basically, the designers put in columns like "Text1","Text2","Text3","Number1","Number2", etc. The users then provide header and description information for these columns, and that is what the app uses for display purposes. This model has the advantage of easy data retrieval, as well as a pre-defined DB schema which should simplify app logic. Data integrity issues remain, however. The other obvious downside is that you will run out of pre-defined columns, which is what you are usually trying to avoid with this type of solution.
As with most design issues, there are tradeoffs to each solution. My experience has been that while many users/clients say they want solutions like these, in reality they are simply trying to ensure they don't get trapped with an app that can't grow with their needs. I have found that there are actually very few places where a design like this is needed. I can almost always create a design that addresses the expansion desires of the client without putting them into the role of database designer.