SQL Server and Over-Indexing Tables
Yes, of course. Every index you create requires maintenance (it needs to be updated for every insert, update and delete operation) and occupies space. Indexes aren't free performance boosts, and should certainly be considered as a trade-off. You should also be very careful about throwing an index on a table to satisfy one query that is called once a week if that table is written all week long. In other words, don't look at the missing index DMVs or a single execution plan and judge the validity of a suggested index in isolation.