ld: fatal: library -lmysqlclient_r: not found
mysqlclient_r is the thread-safe library. It's not available on all platforms, or all installations, apparently. You'll need to reconfigure site.cfg (in MySQLdb-1.2.1 and newer) to have threadsafe = False.
mysql.h: No such file or directory
This almost always mean you don't have development packages installed. On some systems, C headers for various things (like MySQL) are distributed as a seperate package. You'll need to figure out what that is and install it, but often the name ends with -devel.
Another possibility: Some older versions of mysql_config behave oddly and may throw quotes around some of the path names, which confused MySQLdb-1.2.0. 1.2.1 works around these problems. If you see things like -I'/usr/local/include/mysql' in your compile command, that's probably the issue, but it shouldn't happen any more.
ImportError: No module named _mysql
If you see this, it's likely you did some wrong when installing MySQLdb; re-read (or read) README. _mysql is the low-level C module that interfaces with the MySQL client library.
Various versions of MySQLdb in the past have had build issues on "weird" platforms; "weird" in this case means "not Linux", though generally there aren't problems on Unix/POSIX platforms, including BSDs and Mac OS X. Windows has been more problematic, in part because there is no mysql_config available in the Windows installation of MySQL. 1.2.1 solves most, if not all, of these problems, but you will still have to edit a configuration file so that the setup knows where to find MySQL and what libraries to include.
ImportError: libmysqlclient_r.so.14: cannot open shared object file: No such file or directory
The number after .so may vary, but this means you have a version of MySQLdb compiled against one version of MySQL, and are now trying to run it against a different version. The shared library version tends to change between major releases.
Solution: Rebuilt MySQLdb, or get the matching version of MySQL.
Another thing that can cause this: The MySQL libraries may not be on your system path.
Solutions:
set the LD_LIBRARY_PATH environment variable so that it includes the path to the MySQL libraries.
set static=True in site.cfg for static linking
reconfigure your system so that the MySQL libraries are on the default loader path. In Linux, you edit /etc/ld.so.conf and run ldconfig. For Solaris, see Linker and Libraries Guide.
ImportError: ld.so.1: python: fatal: libmtmalloc.so.1: DF_1_NOOPEN tagged object may not be dlopen()'ed
This is a weird one from Solaris. What does it mean? I have no idea. However, things like this can happen if there is some sort of a compiler or environment mismatch between Python and MySQL. For example, on some commercial systems, you might have some code compiled with their own compiler, and other things compiled with GCC. They don't always mesh together. One way to encounter this is by getting binary packages from different vendors.
Solution: Rebuild Python or MySQL (or maybe both) from source.
ImportError: dlopen(./_mysql.so, 2): Symbol not found: _sprintf$LDBLStub Referenced from: ./_mysql.so Expected in: dynamic lookup
This is one from Mac OS X. It seems to have been a compiler mismatch, but this time between two different versions of GCC. It seems nearly every major release of GCC changes the ABI in some why, so linking code compiled with GCC-3.3 and GCC-4.0, for example, can be problematic.
Starting with 1.2.0, MySQLdb disables autocommit by default, as required by the DB-API standard (PEP-249). If you are using InnoDB tables or some other type of transactional table type, you'll need to do connection.commit() before closing the connection, or else none of your changes will be written to the database.
Conversely, you can also use connection.rollback() to throw away any changes you've made since the last commit.
Important note: Some SQL statements -- specifically DDL statements like CREATE TABLE -- are non-transactional, so they can't be rolled back, and they cause pending transactions to commit.
OperationalError: (1251, 'Client does not support authentication protocol requested by server; consider upgrading MySQL client')
This means your server and client libraries are not the same version. More specifically, it probably means you have a 4.1 or newer server and 4.0 or older client. You can either upgrade the client side, or try some of the workarounds in Password Hashing as of MySQL 4.1.