<p>I have an index on columns A, B, C, D of table T</p>

<p>I have a query that pulls from T with A, B, C in the WHERE clause.</p>

<p>Will the index be used or will a separate index be needed that only includes A, B, C?</p>

in Oracle databases this is called a
Composite Index
( 12g docs but valid for earlier versions)
Composite indexes can speed retrieval of data for SELECT statements in which the WHERE clause references all of the leading portion of the columns in the composite index. Therefore, the order of the columns used in the definition is important. In general, the most commonly accessed columns go first.
so in your case, Yes. the index would/could be used.  this could be verified by using an explain plan.
if MS SQLSERVER is different (and i suspect it might) you'll need a new answer.
Edit:
Should also mention it will only
consider
the index for use.. that does not necessarily mean it WILL use it.
Edit2:
Oracle 11g and later now has an option that will allow it to skip columns in an index. so a query on A,B and D might still use the index