> So if I want to use MySQL, I'll have to go back to an older image than 
> 3.7gamma, right?  Do you happen to know which image would be preferred?

Of course, you can use the ODBC package and install a MySQL ODBC driver.  I use this to access MySQL and SQL Server in my job duties (on 3.7).

> And if I want to use a serious relational database with the current 
> image it would have to be PostgreSQL, right?

Or any relational database that provides an ODBC-provider -- which would be all the serious ones (and some not-so serious ones).
 
> Which of these approaches do most people use when they want to use a 
> database with Squeak?  Or do people use databases with Squeak?

We do a ton of work with databases and Squeak 3.6 / 3.7.  That's all I do!  Select this, insert that, delete (whoops)....rollback

> I know I could consider some kind of object oriented 
> database like GOODS, but that seems to offer only persistence, not the 
> automatic indexing and fast searching on any part of the data that SQL 
> databases can do.

We also use GOODS quite a bit when we have options to be more efficient in our development and not bridge the object-relational divide.  Of course, with GOODs the onus for indexing rests with you (e.g. keep the necessary maps as objects in the database as well).  Indexing is easy (with dictionaries or btrees), but the more general problem is keeping your indexes up-to-date.  GOODS supports fast searching if you utilize the indexes you already have (like relational databases) -- and it is slow if you perform "full table scans" (like relational databases).

Regards,

John