I am generally not in favor of red dot sights on carry pistols. My reasons for this are pretty much the same as what other posters have stated. Red dots sights actually slow people down for quick close work, especially when shooting from awkward or one-handed positions. And the strong advantages of red dot sights for distance shooting are not applicable to most people's defensive requirements. I am very aware of the difficulties that poor eyesight can cause for pistol shooting, but my standard for defensive shooting is to hit a paper plate at 7 yards, and most people can do that with iron sights.
If someone has severe eyesight problems, or a specific need for distance precision, then I can imagine situations where a red dot might be a good choice for carry. But that would require careful thought about the compromises being made and the additional training required.
These views are partly based on my own own observations, but I have also been influenced by Grant Cunningham, who comments briefly on red dot sights here:
Your Hump Day Reading List for March 23, 2016 - www.GrantCunningham.com www.GrantCunningham.com
Grant also links to the following article:
The Fall of the Red Dot
Some of you will be familiar with Grant as a well renowned revolversmith, but he is also a highly regarded defensive trainer.
I would also add that I have a different view about red dot sights on rifles. On a close quarters defensive rifle, the compromises are different, and I strongly recommend the use of a red dot. However, I always tell people that the budget for a "duty" quality red dot is $500 or more. The best quality red dots are extremely rugged, but I have not seen this quality in mid-priced models.
The trijicon RMR sights, which have been recommended above, have a strong reputation. There are two types of these sights: battery operated LED, and dual illuminated with fiber optic and tritium. Both types are good, but each also has disadvantages. The pros and cons to too long for me to discuss here, but if you are considering these it is worth taking time for research.
There may be other small red dots which are equally reliable, but I have not personally examined them. I would budget at least $600 for sight and mount if I needed something I could rely on.