In terms of being issued by the US Army to frontline infantry, pistols were actually not as common as you would think. Pistols were mainly issued to mortar and machine gunners and their assistants, and antitank gunners. Very high (battalion and regimental) staff officers were also issued pistols, in lieu of carbines. In a typical US infantry regiment (3,207 men) there were only 293 pistols authorized by the TO&E, in contrast with 836 M1 carbines and over 1,800 M1 rifles.

In practice the TO&E was not as rigidly followed, and soldiers sometimes scavenged (or stole) whatever weapons they felt would best suit them, and this often meant a pistol as a backup to a bulky full-sized rifle. Many soldiers also captured enemy weapons as souvenirs, and a Luger pistol was a coveted prize for many a GI.

In the television series The Pacific, Marine Pfc. Eugene Sledge receives a care package from his father containing a Colt New Service .45 caliber revolver; he uses the weapon twice throughout the series. Police departments and other community organizations, especially if the soldier was from a small town, often sent care packages overseas as a show of support, some containing weapons for the soldier to use (invariably mostly pistols)

Sources:

TO 7-11 Infantry Regiment, dated 26 February 1944 http://www.militaryresearch.org/7-11%2026Feb44.pdf

TO 7-15 Infantry Battalion, dated 26 February 1944 http://www.militaryresearch.org/7-15%2026Feb44.pdf

TO 7-16 Headquarters and Headquarters Company, Infantry Battalion, dated 26 February 1944 http://www.militaryresearch.org/7-16%2026Feb44.pdf

TO 7-17 Rifle Company, dated 26 February 1944 http://www.militaryresearch.org/7-17%2026Feb44.pdf

TO 7-18 Heavy Weapons Company, dated 26 February 1944 http://www.militaryresearch.org/7-18%2026Feb44.pdf

Can't say for others but Finnish soldiers. The military passport - a document received upon completion of national service and containing the instructions for mobilization - from the 1930s explicitly tells the reservist to bring a pistol when mobilized, if he owned one.

""The reservist has to take with him: ...

"Proper boots or skiing boots, two pairs of underwear, woolen shirt, towel, military style outerwear or in its absence usable outdoors outerwear, needle and thread, pocket pistol with ammunition, binoculars and compass and additionally during winter skis and ski poles."

I haven't seen any explicit estimates of how common the personal sidearms were, but I think a fair guess that not more than one in five owned a pistol. Rifles and shotguns were fairly common home-owned firearms, pistols not so much. Wealthier folks were more likely to own a pistol, but they were more often trained as reserve officers.

In addition to that, particularly during the Continuation War (1941-44) many soldiers captured Soviet pistols for their own use. Again, I don't have estimates as this was a bit illegal: captured weapons were supposed to be turned over to the Army.

It should be noted that even if pistols were available, soldiers didn't always want to carry them. As one lessons learned document reviewing the gear for long range patrols - who had considerable leeway in selecting their own equipment - notes (whew, this is getting a bit of use):

"The importance of short weapon [pistol] as everyman's back-up weapon should not be overestimated. It is of course good to have in case of getting lost, but otherwise it is sufficient that some men [in a patrol of 3 to 15 men] carry such a weapon."

(Source)

Probable reasons are that pistols add weight yet their accuracy and hence usefulness is fairly limited. As someone once noted, "there's little you can do with a pistol that you can't do better with a rifle." Or with Suomi SMG.

I can speak on few accounts from American Paratroopers of the 101st Airborne Division and I know of at least two troopers that carried weapons from home. Don Burgett of A company, 506 Parachute Infantry Regiment, carried a chrome plated Colt 1911 his father had sent to him while staging for the Normandy Invasion in England.

The other trooper was Floyd Talbert of E Company (same as Band of Brothers) of the 506 PIR. His mother sent a Colt .45 revolver given as a gift from the police chief of his hometown in Kokomo, Indiana.

Sources: "Curahee" by Donald A. Burgett and "In the Footsteps of the Band of Brothers" by Larry Alexander

Prior to the second world war Canadian officers were expected to provide their own pistols at their own expense.Up into the second world war this was still an option.