The sweet spot of ORMs
ORMs are useful for automating the 95%+ of queries where they are applicable. Their particular strength is where you have an application with a strong object model architecture and a database that plays nicely with that object model. If you're doing a new build and have strong modelling skills on your team then you will probably get good results with an ORM.
You may well have a handful of queries that are better done by hand. In this case, don't be afraid to write a few stored procedures to handle this. Even if you intend to port your app across multiple DBMS platforms the database dependent code will be in a minority. Bearing in mind that you will need to test your application on any platform on which you intend to support it, a little bit of extra porting effort for some stored procedures isn't going to make a lot of difference to your TCO. For a first approximation, 98% portable is just as good as 100% portable, and far better than convoluted or poorly performing solutions to work around the limits of an ORM.
I have seen the former approach work well on a very large (100's of staff-years) J2EE project.
Where an ORM may not be the best fit
In other cases there may be approaches that suit the application better than an ORM. Fowler's Patterns of Enterprise Application Architecture has a section on data access patterns that does a fairly good job of cataloguing various approaches to this. Some examples I've seen of situations where an ORM may not be applicable are:
On an application with a substantial legacy code base of stored procedures you may want to use a functionally oriented (not to be confused with functional languages) data access layer to wrap the incumbent sprocs. This re-uses the existing (and therefore tested and debugged) data access layer and database design, which often represents quite a substantial development and testing effort, and saves on having to migrate data to a new database model. It is often quite a good way wrapping Java layers around legacy PL/SQL code bases, or re-targeting rich client VB, Powerbuilder or Delphi apps with web interfaces.
A variation is where you inherit a data model that is not necessarily well suited to O-R mapping. If (for example) you are writing an interface that populates or extracts data from a foreign interface you may be better off working direclty with the database.
Financial applications or other types of systems where cross-system data integrity is important, particularly if you're using complex distributed transactions with two-phase commit. You may need to micromanage your transactions better than an ORM is capable of supporting.
High-performance applications where you want to really tune your database access. In this case, it may be preferable to work at a lower level.
Situations where you're using an incumbent data access mechanism like ADO.Net that's 'good enough' and playing nicely with the platform is of greater benefit than the ORM brings.
Sometimes data is just data - it may be the case (for example) that your application is working with 'transactions' rather than 'objects' and that this is a sensible view of the domain. An example of this might be a financials package where you've got transactions with configurable analysis fields. While the application itself may be built on an O-O platform, it is not tied to a single business domain model and may not be aware of much more than GL codes, accounts, document types and half a dozen analysis fields. In this case the application isn't aware of a business domain model as such and an object model (beyond the ledger structure itself) is not relevant to the application.