First, they absolutely must have shown that they are reliable and over the long-term and with copious amounts of ammunition. Included under "reliability" is the weapon's ability to handle varied types of ammunition in its caliber. In other words, it should be able to handle round nose, semiwadcutter or jacketed hollow point without stuttering.
Though I am sometimes accused of being "too concerned" with accuracy, all that I personally require is that the handgun be capable of better groups than I am. In other words, if I can shoot better than the individual firearm, I'm no longer interested in it. Happily, I can report that there has been very few such firearms in my past but they have popped up now and again!
To be a favorite with me, the firearm must not be particularly fragile. It should hold up to quite a bit of shooting without constant parts breakage; in other words, I do not want to be on a first name basis with any gun company's customer service section. This does not mean that I intend to abuse the firearm or treat it to a "torture test" of firing to see just how many rounds can go through it without cleaning, etc.
Speaking only for myself, to be a favorite, the gun needs to not only be very comfortable but have that special "look" as well. It is not necessary that it be a thing of beauty to anyone else but me.
It may or may not have been present at some unique time in the past, either mine or another person's. For example, a handgun that kept a knife off of me before I retired from policing have some special significance, but again it might not. At the same time, a handgun simply owned by another person close to me might very well be a favorite simply for that reason.
This S&W Model 19 is nothing unique and is one I bought NIB in the '70's for my father. With his passing, it returned to me and for obvious reasons is a favorite. It will never be sold.
Another favorite of mine is my first Browning 9mm Hi Power. I have had this one for decades, purchasing it new in 1971. It has fired many thousands of rounds and is on its original parts other than for spring replacement.
Affectionately known as "Number 1", this Hi Power has been customized over 30 years ago and serves well today. It has been used mostly for fun but did strongly discourage a burglar on one ocassion.
One of my favorite 1911 pattern pistols is a Springfield Armory Mil-Spec. This .45 appears to be nothing special until it is shot. Internals were worked over by Teddy Jacobson of "Actions by "T" out of Sugarland, Texas. This thing has never stuttered even one time since it was bought new. It's had roughly 5000 shots fired. (That does NOT mean 5000 shots between cleanings. About the most it's gone was something over 700 full-power loads and I couldn't stand it that filthy any longer.)
Shown with a Remington 870 12-ga. pump shotgun, this Mil-Spec has an exceptionally clean 'working trigger that is almost exactly 4-lbs. After Mr. Jacobson's work, it is just a peach to shoot and enjoy. It is one that I'd not be afraid to use for fun at the range or to protect my home.
Handguns that I use on a daily (and nightly) basis are the compact revolver and snub.
Though from different manufacturers, to me this can be a winning combination. The Ruger SP101 (top) is chambered for .357 magnum while the S&W Model 642 (bottom) holds only .38 Special. The same HKS speedloader works for both of these 5-shot revolvers. I carry the Ruger with Corbon 125-gr. DPX "mid-power" 357's and the S&W with Remington 158-gr. LHP +P, which is what the speedloader is filled with. That way the same speedloader can be used with either revolver. The Model 642 is an "always" gun. It may be the primary or it might be a backup, but it is always there. The all-stainless steel SP101 is normally worn with either an IWB or OWB holster while the S&W snub is carried in a Galco pocket holster.
Another favorite for me has been the S&W "CS-1" (Customs Service) .357 revolver with a 3" barrel. These are not seen all that often and usually have exceptionally nice double-actions out of the box.
This S&W CS-1 came with a very nice double-action trigger-pull and has is wearing inexpensive nylon "Hideout" grips. (I textured the surface on these using an engraving pencil.)
There are others to be sure, but these are some handguns that have served me well and continue to do so. Some are favorites for purely sentimental reasons while others simply do what I want each and every time the trigger is pressed. Some fill a perceived role so well that no effort has been made for replacement.
How about you? Do you have few selected handgun favorites?
I suspect that most of us do.