<p>What is the difference between creating one index across multiple columns versus creating multiple indexes, one <em>per</em> column?</p>
<p>Are there reasons why one should be used over the other?</p>
<p>For example:</p>
<pre><code>Create NonClustered Index IX_IndexName On TableName
(Column1 Asc, Column2 Asc, Column3 Asc)
</code></pre>
<p>Versus:</p>
<pre><code>Create NonClustered Index IX_IndexName1 On TableName
(Column1 Asc)

Create NonClustered Index IX_IndexName2 On TableName
(Column2 Asc)

Create NonClustered Index IX_IndexName3 On TableName
(Column3 Asc)
</code></pre>

Yes.  I recommend you check out
Kimberly Tripp's articles on indexing
.
If an index is "covering", then there is no need to use anything but the index.  In SQL Server 2005, you can also add additional columns to the index that are not part of the key which can eliminate trips to the rest of the row.
Having multiple indexes, each on a single column may mean that only one index gets used at all - you will have to refer to the execution plan to see what effects different indexing schemes offer.
You can also use the tuning wizard to help determine what indexes would make a given query or workload perform the best.