PL/pgSQL checking if a row exists

Simpler, shorter, faster: EXISTS.

IF EXISTS (SELECT FROM people p WHERE p.person_id = my_person_id) THEN
  -- do something
END IF;

The query planner can stop at the first row found - as opposed to count(), which scans all (qualifying) rows regardless. Makes a big difference with big tables. The difference is small for a condition on a unique column: only one row qualifies and there is an index to look it up quickly.

Only the existence of at least one qualifying row matters. The SELECT list can be empty - in fact, that's shortest and cheapest. (Some other RDBMS don't allow an empty SELECT list on principal.)

^{Improved with @a_horse_with_no_name's comments.}

Use count(*)

declare 
   cnt integer;
begin
  SELECT count(*) INTO cnt
  FROM people
  WHERE person_id = my_person_id;

IF cnt > 0 THEN
  -- Do something
END IF;

Edit (for the downvoter who didn't read the statement and others who might be doing something similar)

The solution is only effective because there is a where clause on a column (and the name of the column suggests that its the primary key - so the where clause is highly effective)

Because of that where clause there is no need to use a LIMIT or something else to test the presence of a row that is identified by its primary key. It is an effective way to test this.