Fallout 4

To see how many side quest you have completed go to your pip boy-data-stats-quest

In order for a quest to count it cant be a main story mission or a quest from a faction.

Quest that are given to you by people that aren't part of factions are counted as side quest.

To find them easily go to any of the main cities and talk to anyone with names. Some of them will give you quest. Sometimes while you are walking around you will find a new radio station, they can give you side quests.

Here is a list of quest for fallout 4 http://fallout.wikia.com/wiki/Fallout_4_quests.
Look under side quest for a list of what quest you need.
Also some of those quest are miscellaneous which do not count.

These are the quest that i think are side quest. If you know any more or if i was wrong post it in the comments.

Quick and Easy Quest
Short Stories - Vault 81, talk to Katy
The Devils Due - dead body near Museum of Witchcraft / misc. obj. to investigate Museum of Witchcraft
Vault 81 - enter Vault 81
In Sheep's Clothing - Diamond City, after you complete the game fast travel to a place near Diamond City and walk there, when you enter go down the stairs and talk to the group of people
Order Up - Drumlin Diner, talk to the Wolfgang
Story of the Century - Diamond City, talk to Piper
Painting the Town - Diamond City, talk to Abbot
The Disappearing Act - Diamond City, pick up Earl Sterling file in Nick Valentines Agency, might have to save Nick first
Cambridge Polymer Labs - Cambridge Polymer Labs, talk to Molly



The Silver Shroud - listen to the Silver Shroud Radio near Goodneighbor
Special Delivery - talk to Edward Deegan at Bunker Hill/ talk into intercom at Cabot House
Emogene Takes a Lover - complete Special Delivery
The Secret of Cabot House - complete Emogene Takes a Lover
Hole in the Wall - Vault 81, give doctor blood, leave and come back to doctor
Confidence Man - Diamond City, talk to Travis, gaurd will give you a misc. obj. to talk to Vadim
Last Voyage of the U.S.S Constitution - board the U.S.S Constitution
Curtain Call - listen to Trinity Radio near Trinity Tower
The Big Dig - Goodneighbor, talk to Bobbi, she is at the end of an alleyway behind a door
Trouble Brewin' - Goodneighbor, talk to Rufus Rubins
Human Error - Covenant, talk to Honest Dan
Vault 75 - enter Vault 75
Long Time Coming - Have Nick Valentine be your companion, After his third time asking to talk he will eventually give you the quest
Diamond City Blues - Diamond City, Colonial Taphouse, watch Paul get beat up, talk to him around town
Out in Left Field - Diamond City, talk to Moe Cronin
The Gilded Grasshopper - Diamond City, pick up Marty Bullfinch file in Nick Valentines Agency, might have to save Nick first
Pickman's Gift - get misc. obj. to investigate Pickman's Gallery from any City / go to Pickman's Gallery
Public Knowledge - Goodneighbor, talk to daisy
Emergent Behavior - have Curie be your follower and the first time she asks to talk you will get the quest - not sure if this counts