I updated 2.0 to 2.2, no db change. Server was unable to start. From the log:

Starting Zabbix Server. Zabbix 2.2.4 (revision 46772).
...
current database version (mandatory/optional): 02010000/02010000
required mandatory version: 02020000
optional patches were found
starting automatic database upgrade
completed 0% of database upgrade
completed 1% of database upgrade
completed 2% of database upgrade
completed 3% of database upgrade
completed 4% of database upgrade
completed 5% of database upgrade
completed 6% of database upgrade
[Z3005] query failed: [1091] Can't DROP 'httptest_2'; check that column/key exists [drop index httptest_2 on httptest]
database upgrade failed

I was able to start zabbix server and successfully upgrade database by issuing the following mysql command:
CREATE INDEX httptest_2 on httptest (name);

It would be nice if database upgrade did not fail if index which is going to be dropped does not exist.