with MySQL, are multiple single column indexes faster than one multi-column index?
SHORT ANSWER

Only as a last resort

LONG ANSWER
Having multiple indexes can be a rather arduous adventure for MySQL Query Optimizer.
I have written about this before

Sep 18, 2012 : How are multiple indexes used in a query by MySQL?
Apr 19, 2014 : Optimizing indexes (Under the Heading ANSWER TO QUESTION #2)

In essence, MySQL will do lookups along multiple indexes and perform an index merge of the results. This would only be done as a last resort if there are no compound indexes that are usable for your query's WHERE, GROUP BY, and ORDER BY clauses.
The order of the columns in the multiple-column index also has a bearing. If you have the following:

Table with indexes (a),(b),(c)
Same table with index (a,b,c)

The three-column index would be better if the WHERE, GROUP BY, and ORDER BY clauses harness the indexed columns in the order inside the index (a,b,c). Anything different combination could possibly result in an index range scan of (a,b,c). Next best choice could be full index scan of (a,b,c) . If these are not possible, the last resort becomes the merge of searching (a),(b),(c) separately.