You'd get orders of magnitude more improvement by changing all tables to make sure they have the best clustered index for overall performance and based on how data is (almost) always searched for, rather than just rebuilding the indexes you have now. Hint: the best clus index is most often not on an identity column.
For example, for child tables, it's almost always best to have the parent's key first. Thus, the order items table would be clustered first on the order_id column, and only then the item identity. Since the order_id is an identity (and the clustering key, btw), on the orders table, the item table is generally inserted in order as well. But now the join between the tables is vastly more efficient, typically a MERGE JOIN, reading joined contiguous rows from the order items table and SQL "knows" they're contiguous. With an identity cluster on the items, SQL has to go thru a non-clus index to do the joins and SQL assumes the rows aren't in contiguous order (the only safe assumption, since they may not be).
Similarly, intersection tables should typically be keyed the actual keys of the parent tables, not by a meaningless identity.
Thus, since there are far more child / dependent tables than "master" / parent tables, it's only logical that the majority of tables are best clustered on something other than identity the vast majority of the time.
Only after determining and setting the best clus index, should you then review all the non-clus indexes. Often many of them can now be removed, since they are keyed first by what is now the clus key(s).
The really complex part is determining which non-clus indexes should be combined. There's some art with the science there. Scanning an existing index can be much better than creating a separate index, but you naturally don't want to get too carried away with it.
A specific example(s) would be much clearer. Generalities provide some guidance, but nothing like walking thru a few real-world situations.
SQL DBA,SQL Server MVP(07, 08, 09) Prosecutor James Blackburn, in closing argument in the Fatal Vision murders trial: "If in the future, you should cry a tear, cry one for them [the murder victims]. If in the future, you should say a prayer, say one for them. And if in the future, you should light a candle, light one for them."