This may be better on the Programmers SE, but I'll answer here.
CRUD stored procedures used to be, and sometimes still are, the best practice for data persistence and retrieval on a SQL DBMS. Every such DBMS has stored procedures, so you're practically guaranteed to be able to use this solution regardless of the coding language and DBMS, and code which uses the solution can be pointed to any DB that has the proper stored procs and it'll work with minimal code changes (there are some syntax changes required when calling SPs in different DBMSes; often these are integrated into a language's library support for accessing SPs on a particular DBMS). Perhaps the biggest advantage is centralized access to the table data; you can lock the tables themselves down like Fort Knox, and dispense access rights for the SPs as necessary to more limited user accounts.
However, they have some drawbacks. First off, SPs are difficult to TDD, because the tools don't really exist within database IDEs; you have to create tests in other code that exercise the SPs (and so the test must set up the DB with the test data that is expected). From a technical standpoint, such a test is not and cannot be a "unit test", which is a small, narrow test of a small, narrow area of functionality, which has no side effects (such as reading/writing to the file system). Also, SPs are one more layer that has to be changed when making a needed change to functionality. Adding a new field to a query result requires changing the table, the retrieval source code, and the SP. Adding a new way to search for records of a particular type requires the statement to be created and tested, then encapsulated in a SP, and the corresponding method created on the DAO.
The new best practice where available, IMO, is a library called an object-relational mapper or ORM. An ORM abstracts the actual data layer, so what you're asking for becomes the code objects themselves, and you query for them based on properties of those objects, not based on table data. These queries are almost always code-configurable, and are translated into the DBMS's flavor of SQL based on one or more "mappings" that you define between the object model and the data model (objects of type A are persisted as records in table B, where this property C is written to field D).
The advantages are more flexibility within the code actually looking for data in the form of these code objects. The criteria of a query is usually able to be customized in-code; if a new query is needed that has a different WHERE clause, you just write the query, and the ORM will translate it into the new SQL statement. Because the ORM is the only place where SQL is actually used (and most ORMs use system stored procs to execute parameterized query strings where available) injection attacks are virtually impossible. Lastly, depending on the language and the ORM, queries can be compiler-checked; in .NET, a library called Linq is available that provides a SQL-ish keyword syntax, that is then converted into method calls that are given to a "query provider" that can translate those method calls into the data store's native query language. This also allows queries to be tested in-code; you can verify that the query used will produce the desired results given an in-memory collection of objects that stands in for the actual DBMS.
The disadvantages of an ORM is that the ORM library is usually language-specific; Hibernate is available in Java, NHibernate (and L2E and L2SQL) in .NET, and a few similar libraries like Pork in PHP, but if you're coding in an older or more esoteric language there's simply nothing of the sort available. Another one is that security becomes a little trickier; most ORMs require direct access to the tables in order to query and update them. A few will tolerate being pointed to a view for retrieval and SPs for updating (allowing segregation of view/SP and table security and the ability to restrict the retrievable fields), but now you're mixing the worst of both worlds; you still have to define mappings, but now you also have code in the data layer. The easiest way to overcome this is to implement your security elsewhere; force applications to get data using a web service, which provides the data using the ORM and has specific, limited "front doors". Also, many ORMs have some performance problems when used in certain ways; most are designed to "lazy-load" data, where data is retrieved the moment it's actually needed and not before, which increases up-front performance when you don't need every record you asked for. However, when you DO need every record you asked for, this creates extra round trips. You have to structure queries in specific ways to get around this expected use-case behavior.
Which is better? You have to decide. I can tell you now that using an ORM is MUCH easier to set up and get working correctly than SPs, and it's much easier to make (and limit the scope of) changes to the schema and to queries. In the modern development house, where the priority is to make it work first, and then make it perform well and/or be secure against intrusion, that's a HUGE plus. In most cases where you think security is an issue, it really isn't, and when security really is an issue, putting the solution in the DB layer is usually the wrong place, because the DBMS is the very last line of defense against intrusion; if the DBMS itself has to be counted on to stop something unwanted from happening, you have failed to do so (or even encouraged it to happen) in many layers of software and firmware above it.