Should I rely on Database Engine Tuning Advisor for creating indexes?
Database Engine Tuning Advisor, like the DMVs such as sys.dm_db_missing_index_details and sys.dm_db_missing_index_groups give you a good place to start, as does the dmv sys.dm_db_index_usage_stats, to see which indexes are not being utilized and could be dropped.

However, these tools are never going to be as good as a skilled DBA making rational descisions about what indexes are really required. For example, DTA might recommend dropping an index that is hardly ever used and is expensive to maintain, but with business knowledge, you know that this index is key to running the monthly payroll.

In short - Use these tools to get a head start, but rely on your business knowledge, and performance troubleshooting skills as the final descision maker.