Q:

What is the lowest altitude where the effect of lack of acclimatization can be observed?

What is the lowest altitude where the effect of lack of acclimatization can be observed?
I've heard that generally we speak about the need for acclimatization over 3000 meters (9800 feet). Are the negative effects, such as significantly decreased performance, headaches etc., observed on at least a significant part of the population at the lower altitudes, for example 2000 meters (6500 feet)?

A:

The best research I can find is from  The Institute of Altitude Medicine in the US. 
Quoting studies on skiers visiting high resorts in Colorado:

AMS (Acute Mountain Sickness) can afflict any visitor sleeping higher than 6000 feet. In
  Colorado, between 15 and 40% of visitors sleeping at 8000 ft or higher
  get AMS, with the incidence the highest at the highest resorts.

The subjects were people who had come straight up from low altitude in a single day. Subjects who spent a night at an intermediate altitude experienced far fewer symptoms.
So it seems that people can experience full AMS as low as 6000ft (1800 meters).
Headache alone doesn't qualify as AMS - there have to be additional symptoms such as loss of appetite, vomiting, weakness, dizziness, fatigue, or difficulty sleeping. 
So if people experience full AMS at 6000 ft, we can assume that the most susceptible people will experience altitude headaches at an even lower altitude.
I can testify to this from personal experience. On the first day at altitude I tend to feel a bit of headache and nausea at around 5500 ft if I'm ascending with a pack. I try to sleep no higher than 6000 feet, and by the next day I'm usually fine and ready to go much higher.

A:

According to the International Society for Mountain Medicine, in its article Normal Acclimitization:

Acclimatization is the process of the body adjusting to the decreased
  availability of oxygen at high altitudes. It is a slow process, taking
  place over a period of days to weeks.    High altitude is defined as: 
•High Altitude: 1500 - 3500 m (5000 - 11500 ft)  
•Very High Altitude: 3500 - 5500 m (11500 - 18000 ft) 
•Extreme Altitude: above 5500 m
Practically speaking, however, we generally don't worry much about
  elevations below about 2500 m (8000 ft) since altitude illness rarely
  occurs lower than this.

If a user of this site pooh-poohs the need for acclimatization at the elevation of Denver, they should bear in mind that they are young(ish), in good shape, accustomed to sustained physical exertion and probably have often been at much higher elevations. 
As for peak athletic performers, according to Sports Fitness Advisor:

Acclimatization to altitude has become an important part of the
  preparation process for athletes competing above 1500m (4921ft).

This article later mentions the 1968 Olympic Games in Mexico City and says:

It takes approximately two weeks to adapt to the changes associated
  with the hypobaric conditions at 2268m (7500ft), roughly that of
  Mexico City.

Edit in Response to Comment by @Tullochgorum  
The OP did not ask about AMS, but about acclimatization.  People in good physical shape, like most users here, will land at Denver and will not notice the effect the altitude has on them unless they have to run a goodly distance to make their connection.  So they might pooh-pooh the idea of an effect in Denver.   In contrast, the effect on someone in poor shape might be very noticeable (needs assistance at Denver airport, doesn't need assistance at Dulles) and a top athlete might be so attuned that he might notice any effect immediately.

