The points below summarizes the situation as of August 2013:
1) We support MySQL versions (whether official MySQL builds or 'fork' builds) from 4.1.x and higher. Support for 3.23 and 4.0 servers stopped with 11.2x and you will not be able to connect to such from SQLyog 11.2x. Also please note than any version before 5.1 is now out of active support and you should consider to upgrade to a recent and still-supported version if you are using 4.1 or 5.0 servers.
2) for any supported 'major' versions we "do not care" about issues with alpha/beta/RC versions if issue can be resolved by upgrading to a stable/GA version in the same tree.
3) If you for some reason need to stay with 4.1, we recommend 4.1.20 or higher. Some Linux distributions (most important RHEL4) originally shipped with 4.1.10. This version had serious bugs the handling of unicode character sets introduced in 4.1 (most of issue referred were fixed in 4.1.12). Official RHEL 4.1.20 builds are available for upgrade by RHEL4 users.
4) for 5.0 specifically we recommend 5.0.67 or higher - or even better 5.0.96. 5.0.96 is the latest 5.0 version currently and is probably also the last 5.0 version that will ever be released.
5) for 5.1 specifically you should use at least 5.1.35 or higher. Around version 5.1.30 the InnoDB code in MySQL was replaced from what was known as the 'built-in InnoDB' to the 'InnoDB plugin'. This caused some turbulence and introduced bugs. 5.1.35 is the oldest 5.1 version where those bugs are mostly fixed. But observe that 5.1 will probably also not be supported anymore soon. At the moment of writing latest 5.1 release is 5.1.71 and we recommend to keep 5.1 server updated to a recent release (5.1.70+ currently). For the MariaDB 5.2 and 5.3 'forks' (that are based on MySQL 5.1 with additional features added) you should also ensure that the MySQL 'parent' for the MariaDB release you use is recent.
6) for 5.5 specifically we recommend 5.5.32 or higher.
7) for 5.6 specifically we recommend 5.6.13 (the latest 5.6 release currently). There are a lot of internal changes in the server between 5.5 and 5.6 and in particular if you use replication options introduced recently you can expect important bug fixes and performance improvements in new releases. So it is your own interest to keep the server updated.
8) for all stable/GA releases (also those listed as recommended above) it also may happen that we will not resolve an issue if an upgrade to a later version resolves the issue. It depends on the nature and seriousness of the issue and the effort required to fix or 'work around' the issue with the older version.
9) for versions that are only available as alphas/betas/RCs (currently anything higher than 5.6 - MySQL 5.7 and MariaDB 10) we will consider only the most recent version released at the time of reporting. There is no guarantee that we will resolve an issue with those if we do not consider the issue critical. We may decide to 'wait and see' as there are often significant change of functionality with new releases of those early builds.
10) and finally with versions only available from special branches and servers built from with latest committed source from the source code development trees we will generally not take action if no other server build is affected and if it is not obvious that there is a bug that should be fixed under any circumstance.