Even if I don’t remember every single one of those I can at least spark a discussion. Unlike most people I don’t mind the Bond theme in the new game as gadgets or (“equipment” as it’s called) are very interesting and useful. Anyway, in Absolution there was an achievement for your first throwable kill (if I remember correctly “It’s All In The Wrist”) and it is a reference to Octopussy where Bond uses Kamal Khan’s rigged dice to win the game. Because I don’t want to post an Absolution photo, you get Roger Moore in a white dinner jacket.
The pose that they chose for the promotional art is a reference to the cover of the book “Blood, Sweat and Bond” but from a different angle. It is also a reference to the poster from Tomorrow Never Dies.
a bit of this…
a chunk of that…
The dinner suit that 47 wears in the Paris mission appeared to have been directly influenced by the one found most notably in Thunderball and Skyfall. (Thanks to @Reaper for pointing it out)
@Danger_dog_guy_7 for pointing it out and to @Bjornie47 for providing the photo)
The turtleneck that 47 is wearing in the training missions resembles the one worn by Pierce Brosnan in Die Another Day.
The Faberge egg (The Ivory White) that 47 has to retrieve in the 8th Elusive Target, The Broker, bears much resemblance (albeit a different color scheme) to the one found in Octopussy (The Property of a Lady). It’s also featured in a very similar scenario, where both of them are found during an auction. (Thanks to @Keller for pointing it out)
The ICA logo bears much resemblance to the MI5 logo (not the MI6 one @JJoa74) and even feautures a 007 below the crown (at least in Hitman: Codename 47)
The most obvious one would have to be the WA2000 that 47 uses in every game since Codename 47 (except Absolution). Nice to see that the developers appreciated the Timothy Dalton era. (Thanks to @jackdagger for pointing that out)
The Final Test features lots of references to Goldeneye and The Living Daylights. It has a spy named Janus (named after the two faced Roman god) and a chess player defecting to the soviets and wanting to bring his girlfriend along (the exact opposite plan from Giorgi, who wanted her dead). (Thanks to @jackdagger for pointing that out).
The Tomorrow Never Dies theme is used in Blood Money even if it sounds nothing like the finished product. (Thanks to @jackdagger for pointing that out)
47 has the option to leave Lenny behind in the desert but instead of giving him motor oil, he lets him die (or commit suicide with his Swiss Derringer). 007 used the same technique in Quantum of Solace.
Diana gives 47 a briefing in a confession booth like the one Q did in For Your Eyes Only. (Thanks to @jackdagger for pointing that out)
Be sure to write about the ones you spotted!