Will more indexes on a table affect performance?
An INSERT will touch the clustered index, or heap, and every nonclustered index.  An UPDATE will touch the clustered index, or heap, and every nonclustered index that contains, at either the key or the leaf level, the column being updated.  A DELETE will touch the clustered index, or heap, and every nonclustered index.  An exception to these statements is when a record is filtered out of the index.

A general rule of thumb is that the more indexes you have on a table, the slower INSERT, UPDATE, and DELETE operations will be.  This is why adding indexes for performance is a trade off, and must be balanced properly.

Hope this helps,

Matt