Over-use and/or dependence on stored procedures.
Some application developers see stored procedures as a direct extension of middle tier/front end code. This appears to be a common trait in Microsoft stack developers, (I'm one, but I've grown out of it) and produces many stored procedures that perform complex business logic and workflow processing. This is much better done elsewhere.
Stored procedures are useful where it has actuallly been proven that some real technical factor necessitates their use (for example, performance and security) For example, keeping aggregation/filtering of large data sets "close to the data".
I recently had to help maintain and enhance a large Delphi desktop application of which 70% of the business logic and rules were implemented in 1400 SQL Server stored procedures (the remainder in UI event handlers). This was a nightmare, primarily due to the difficuly of introducing effective unit testing to TSQL, lack of encapsulation and poor tools (Debuggers, editors).
Working with a Java team in the past I quickly found out that often the complete opposite holds in that environment. A Java Architect once told me: "The database is for data, not code.".
These days I think it's a mistake to not consider stored procs at all, but they should be used sparingly (not by default) in situations where they provide useful benefits (see the other answers).