When you exhaust the upper bound of
INT you will receive, for every new insert:
Msg 8115, Level 16, State 1, Line 1
Arithmetic overflow error converting IDENTITY to data type int.
Arithmetic overflow occurred.
BIGINT is far safer (IMHO) than what some people do - go back to 0 and fill in the gaps, or go to -2 billion and just delay dealing with it until you use the same number of values one more time. If 2 billion rows isn't enough, neither is 4 billion. If you use compression changing the data type for values < 2 billion will actually save you some space.
However you will come across issues if this is part of a primary key constraint, referenced by foreign keys, has other constraints, etc. You'll need to perform some extra work in addition to just changing the data type.