Is it possible to perform multiple updates with a single UPDATE SQL statement?

You can use one statement and a number of case statements

update tbl
  set title = 
    case
      when title in ('a-1', 'a.1') then 'a1'
      when title in ('b-1', 'b.1') then 'b1'
      else title
    end

Of course, this will cause a write on every record, and with indexes, it can be an issue, so you can filter out only the rows you want to change:

update tbl
  set title = 
    case
      when title in ('a-1', 'a.1') then 'a1'
      when title in ('b-1', 'b.1') then 'b1'
      else title
    end
where
  title in ('a.1', 'b.1', 'a-1', 'b-1')

That will cut down the number of writes to the table.

In a more general case, where there could be many hundreds of mappings to each of the new values, you would create a separate table of the old and new values, and then use that in the UPDATE statement. In one dialect of SQL:

CREATE TEMP TABLE mapper (old_val CHAR(5) NOT NULL, new_val CHAR(5) NOT NULL);
...multiple inserts into mapper...
INSERT INTO mapper(old_val, new_val) VALUES('a.1', 'a1');
INSERT INTO mapper(old_val, new_val) VALUES('a-1', 'a1');
INSERT INTO mapper(old_val, new_val) VALUES('b.1', 'b1');
INSERT INTO mapper(old_val, new_val) VALUES('b-1', 'b1');
...etcetera...

UPDATE tbl
   SET title = (SELECT new_val FROM mapper WHERE old_val = tbl.title)
   WHERE title IN (SELECT old_val FROM mapper);

Both select statements are crucial. The first is a correlated sub-query (not necessarily fast, but faster than most of the alternatives if the mapper table has thousands of rows) that pulls the new value out of the mapping table that corresponds to the old value. The second ensures that only those rows which have a value in the mapping table are modified; this is crucial as otherwise, the title will be set to null for those rows without a mapping entry (and those were the records that were OK before you started out).

For a few alternatives, the CASE operations are OK. But if you have hundreds or thousands or millions of mappings to perform, then you are likely to exceed the limits of the SQL statement length in your DBMS.

Working off of Jonathan's answer.

UPDATE tbl
   SET title = new_val
FROM mapper
WHERE title IN (SELECT old_val FROM mapper)
     AND mapper.old_val = tbl.title;

His initial version would require a large number of reads to the mapper table.

If the transformations are as simple as your examples, you could do the update with a little bit of string manipulation:

UPDATE tbl 
SET title = left(title, 1) + right(title, 1) 
WHERE title IN ('a-1', 'a.1', 'b-1', 'b.1')

Would something like that work for you?