There's a rolling giant boulder trap in Legend, prompting "Aww, hell no," from Zip.
There's a rolling giant boulder trap in the Tomb of Qualopec in Anniversary. If that weren't enough it was recently discovered that the giant boulder has a bullwhip and Indiana Jones -type hat flattened onto it.
Also, in the "Angkor Wat" level in The Last Revelation, Lara comes across a spike trap... and in the middle of this spike trap is a skeleton, an Indy-style hat, and a whip. (Quite possibly a Take That.)
The portrait of Kain (as a human) from the Legacy of Kain game series hangs in the lobby of Croft manor in the Crystal Dynamics games.
Lara's Goth outfit has Kain's emblem on her belt buckle as well as Raziel's emblem stamped on her wet suit.
The Soul Reaver is an unlockable special weapon in Legend.
Croft Manor in the Crystal Dynamics games is ripped straight from the live action movies.
The Ark of the Covenant peeking from the lobby crates in the original Tomb Raider.
A large semi-hidden hand at one point in Guardian of Light looks quite similar to the famous Midas hand.
One of the cutscenes in Tomb Raider II has Lara entering a room in the Temple of Xian and spying on the happenings below, which involves members of the Fiama Nera cult ominously chanting. This is definitely a reference to Indiana Jones and the Temple of Doom.
The fate of the RX-Tech mine workers and the entire level "RX-Tech Mines" in Tomb Raider III seem to be inspired by The Thing (1982).
What Could Have Been: The Angel of Darkness was supposed to be the first game in a trilogy. Karel was supposed to survive and be in Turkey, trying to bring back his fellow Nephilim. Kurtis's fate apparently depended on how much the fans liked him (i.e. he would come back if he was really liked, or he would not if he was really disliked). Of course, since The Angel of Darknessfailed miserably, the trilogy idea was scrapped and ideas attached to it along with it - and the original continuity was never continued.
Also in the same game, the watch Lara can find in Francine's apartment was supposed to play a bigger role or at least have a sub plot of its own.
Also, the planned trilogy was going to reveal that the Nephilim and Atlantean races were connected, and Natla was possibly going to be brought Back from the Dead, thus connecting it to the very start of the series.
Jean-Yves was planned to be killed in the beginning of the game instead of Werner, and Werner instead was going to play a much larger role in the game.
Core Design were in the process of making their own remake of the original game (which was looking to be far more faithful than Anniversary) before Eidos dropped them.