Which index types do not support online index rebuilds?
This is in the documentation:


  
  Clustered indexes must be created, rebuilt, or dropped offline when the underlying table contains the following large object (LOB) data types: image, ntext, and text.
   
  Nonunique nonclustered indexes can be created online when the table contains LOB data types but none of these columns are used in the index definition as either key or nonkey (included) columns.
   
  Indexes on local temp tables cannot be created, rebuilt, or dropped online. This restriction does not apply to indexes on global temp tables.
  


Other limitations and considerations are listed as well.