Q:

Is it possible to change a database by SQL SELECT statement? 

We want to allow to an administrator (only) to execute an SQL SELECT statement via Web UI. 
Please note that the administrator is allowed to view all information in a database. 
What are security risks with this approach? 
Is it possible to change somehow a database by SQL SELECT statement (any record or table)? 
added
RDBMS is PostgreSQL

A:

We want to allow to an administrator (only) to execute an SQL SELECT statement via Web UI.  Please note that the administrator is allowed to view all information in a database. 
What are security risks with this approach?  Is it possible to change somehow a database by SQL SELECT statement (any record or table)? 

Well, how do you propose to let them execute SELECT statements?  PostgreSQL doesn't have user-level statement privileges, it has privileges on individual database objects. 
In theory you can absolutely modify the database with SELECT.  Just look at PostgreSQL's function list.  Not to mention the user-defined functions.  The most obvious case is of course nextval, which advances a sequence, or setval which sets a sequence's position. 
However, everything requires rights on the associated database objects.  If you only GRANT the SELECT right on a table (or some subset of the column's tables) then the user won't be able to modify the data in that table directly.  Nor does PostgreSQL provide functions to bypass that restriction built-in.  So simply creating a user with only SELECT rights to some tables and USAGE rights on the schemas they're in should be fine. 
There are some important caveats though.  SECURITY DEFINER user defined functions can do anything the defining user can do so if you have SECURITY DEFINER user defined functions that weren't carefully written you might have opened security holes.  The same is true of user-defined functions written in C - so consider your extensions carefully.  Finally, you need to be extremely careful about any functions written in "untrusted" languages like plpython, plperl, etc (as opposed to plperlu which is sandboxed) as these must be implemented carefully to make sure the calling user can't trick them into doing things they weren't supposed to do. 
If you plan to give a user direct access to write raw SQL you have to be more careful about securing your DB.  Don't GRANT rights to public, and REVOKE them where they're granted by default.  Check security definer functions to make sure they have a SET search_path option defined.  Etc.  It's generally safe, but only if you're careful.