A quick way to see which DBA handlers, without version numbers, that have been built into your version of MySQL on your system, use var_dump with dba_handler() as follows: 
<?php
var_dump ( "dba_handlers()" ); 
?>
Many distros build in these DBA Handlers by default: 
array(5) { [0]=>  string(3) "cdb" [1]=>  string(8) "cdb_make" [2]=>  string(3) "db4" [3]=>  string(7) "inifile" [4]=>  string(8) "flatfile" }
using print and pre tags for readability: 
array(5) {
  [0]=>
  string(3) "cdb"
  [1]=>
  string(8) "cdb_make"
  [2]=>
  string(3) "db4"
  [3]=>
  string(7) "inifile"
  [4]=>
  string(8) "flatfile"
}
Note there are issues with dba_insert and dba_replace without building for either GDBM or QDBM.
  Here are two sources for the list of DBA handlers: (http://www.php-editors.com/php_manual/ref.dba.html and http://dewa03.unep.org/manuals/php_manual/ref.dba.html; )
CDBM & CDB compiles have issues with updates, you can read databases and write new database files, but you will be prevented from using dba_replace() and you may have issues with dba_insert().
NDBM & DBM are depreciated.
DB2, DB3 & DB4 (Berkeley DB Sleepycat Software / Oracle)  Have read online about issues with dba_replace() and db4 specifically. Make sure you test your installation for correct usage of all DBA functions.
SDBM, TDB, TinyCDB were not listed on most of the sources I have found online.  Those DBA handlers and the names of the developers were listed on the QDBM source forge site.  How they interact with dba_replace() I do not know.  You should be aware of their existence.  
GDBM and QDBM are the only other two DBA handlers I am aware of.  Both are reported to allow PHP's dba_replace() function to work correctly so either may be an acceptable option.  The following three restrictions of traditional DBM are not issues for either GDBM or QDBM: 1) a process can handle only one database;  2) the size of a key and a value is bounded;   3) a database file is sparse.
DBA handler benchmark compares QDBM, GDBM, NDBM, SDBM, TDB, CDB, BDB, QDBM-BT-ASC, QDBM-BT-RND, BDB-BT-ASC, BDB-BT-RND can be found here: (http://qdbm.sourceforge.net/benchmark.pdf); 
QDBM seems to offer significant improvements in speed over the other DBA Handlers, test in your environment to verify the results.