If you are selecting a set of columns from the table greater than those covered by the columns in the selected indexes, then you will inevitably incur a bookmark lookup in the query plan, which is where the query processor has to retrieve the non-covered columns from the clustered index using the reference ID from leaf rows in the associated non-clustered index.
In my experience, bookmark lookups can really kill query performance, due to the volume of extra reads required and the fact that each row in the clustered index has to be resolved individually. This is why I try to make NC indexes covering wherever possible, which is easier on smaller tables where the required query plans are well-known, but if you have large tables with lots of columns with arbitrary queries expected then this probably won't be feasible.
This means you only get bang for your buck with an NC index of any kind, if the index is covering, or selects a small-enough data set that the cost of a bookmark lookup is mitigated - indeed, you may find that the query optimizer won't even look at your indexes if the cost is prohibitive compared to a clustered index scan, where all the columns are already available.
So there is no point in creating an index unless you know that index will optimize the result of a given query. The value of an index is therefore proportional to the percentage of queries that it can optimize for a given table, and this can only be determined by analyzing the queries that are being executed, which is exactly what the Index Tuning Wizard does for you.
so in summary:
1) Don't index every column. This is classic premature optimization. You cannot optimize a large table with indexes for all possible query plans in advance.
2) Don't index any column, until you have captured and run a base workload through the Index Tuning Wizard. This workload needs to be representative of the usage patterns of your application, so that the wizard can determine what indexes would actually help the performance of your queries.