Because 'The Matrix' was filmed in Australia the Region 4 (Australia) DVD release includes a more comprehensive Australian based list of credits.
In the UK, 10 seconds of footage was cut from the cinema version to attain a more commercial "15" certificate. The BBFC asked for cuts to 8 head-butts - in the fight between Morpheus and Agent Smith (1 and 3 respectively), and in the subway fight between Neo and Agent Smith (2 each). All UK video and DVD releases featured the same cut print and, even though the commentary was left off the first UK DVD release for this reason, the version featured in the 'Attache Case' box set includes the commentary but still features the cut version. The cuts were finally waived in 2006.
Home video and television versions released after 2004, most notably The Ultimate Matrix Collection box set, and the 2010 Blu-Ray release, have a different color scheme from the 1999 theatrical and home video release. The real-world scenes are given a blue tint and scenes within the Matrix have a heavy green tint.
In the French version, when Neo dies, Trinity says that she loves him and that she is going to bring him back. In the original version she says that she is not afraid anymore because she loves him.
Neo asks if he can dodge bullets: In the French version, Morpheus answers that when he'll be ready, he won't feel them. In the original version, he answers that he won't have to.
In the German version of The Matrix, there is an alternate dialog of the scene on the roof with the agent: After the agent said "only Human", Trinity says "only an agent" instead of "dodge this".
The FOX televised version omits the "There is no spoon" scene before Neo meets The Oracle and cuts down on the multiple shots fired at Neo by Agent Smith at the end; in this version, it only shows Neo shot twice. Some language is, respectively, cut as well.
In the DVD version that was released in Israel, you don't see Mouse running into the kitchen and calling everyone to see Morpheus fights Neo.
Although rated 18, the DVD/video version shown in Ireland is the UK cut version i.e. misses the 10 seconds of head-butts.