Q:

How to list records with date from the last 10 days?

SELECT Table.date FROM Table WHERE date > current_date - 10;

Does this work on PostgreSQL?

A:

Yes this does work in PostgreSQL (assuming the column "date" is of datatype date)
Why don't you just try it?
The standard ANSI SQL format would be: 
SELECT Table.date 
FROM Table 
WHERE date > current_date - interval '10' day;

I prefer that format as it makes things easier to read (but it is the same as current_date - 10).

A:

http://www.postgresql.org/docs/current/static/functions-datetime.html shows operators you can use for working with dates and times (and intervals).
So you want
SELECT "date"
FROM "Table"
WHERE "date" > (CURRENT_DATE - INTERVAL '10 days');

The operators/functions above are documented in detail:

CURRENT_DATE
INTERVAL '10 days'

A:

My understanding from my testing (and the PostgreSQL dox) is that the quotes need to be done differently from the other answers, and should also include "day" like this:
SELECT Table.date
  FROM Table 
  WHERE date > current_date - interval '10 day';

Demonstrated here (you should be able to run this on any Postgres db):
SELECT DISTINCT current_date, 
                current_date - interval '10' day, 
                current_date - interval '10 days' 
  FROM pg_language;

Result:
2013-03-01  2013-03-01 00:00:00 2013-02-19 00:00:00

