BigQuery does not seem to have support for UNION yet:
(I don't mean unioning tables together for the source. It has that.)
Is it coming soon?
If you want UNION so that you can combine query results, you can use subselects in BigQuery:
SELECT foo, bar FROM (SELECT integer(id) AS foo, string(title) AS bar FROM publicdata:samples.wikipedia limit 10), (SELECT integer(year) AS foo, string(state) AS bar FROM publicdata:samples.natality limit 10);
This is almost exactly equivalent to the SQL
SELECT id AS foo, title AS bar FROM publicdata:samples.wikipedia limit 10 UNION ALL SELECT year AS foo, state AS bar FROM publicdata:samples.natality limit 10;
(note that if want SQL UNION and not UNION ALL this won't work)
Alternately, you could run two queries and append the result.