In Sly 3's Blood Bath Bay episode, there's a pirate who has some kind of serious problem with monkeys. In case that was too subtle, later in that same mission Sly has a battle of insults—though no swords are involved, and it doesn't have the same sense of humor as the ones it's clearly referencing.
The Mz. Ruby boss fight in the first game seems to be a Shout Out to Space Channel 5.
From a trailer for Thieves In Time, Bentley exclaims Holy Hand Grenade! when he discovers that the Moat Monster is a robot.
The first time the Cooper van disappears through time in the game's prologue is like that of Back to the Future, complete with leaving behind its license plate spinning.
In Sly 4 during the side-scrolling shooter version of Bentley's hacking sequences, Bentley's avatar is a buffed-up version of himself wielding guns a la Rambo.
Trophy names in Sly 4 reference Final Fantasy, Pirates of the Caribbean, Uncharted, Predator, Evil Dead, Rocky, and Call of Duty.
Murray's training of Bob Cooper in Sly 4 pays a homage to the Rocky movies, and while you're training, Murray shouts quotes from movies like Dodgeball and Star Wars.
Murray: Great shooting, kid, but don't get cocky!
At the end of Chapter 2 in Sly 4, the time-traveling van is seen tumbling through a blue time vortex, then getting struck by lightning, then tumbling faster through a fiery orange vortex — replicating the season 5-7A opening sequence of Doctor Who.
The music on the title screen, which also shows the van flying through the time vortex, is pretty much a Suspiciously Similar Song of the Doctor Who theme crossed with the Sly series main theme.
Collecting 50 Sly Masks will turn Sly's Cane into an OmniWrench.
Similar to above collecting 60 Sly Masks will give turn the Cane into the Amp.