While all the MI movies are first and foremost vehicles for Tom Cruise, MI4 did the best job of showing showing the team working as an ensemble, which was something the original series emphasized. Obviously the movies don't have much in common with the original series, but I appreciated that MI4 remembered this element.
One thing I liked about the first MI movie -- and that the followups lacked --was that the mission was something spies would actually be tasked with. In the original series, the whole point of the IMF was that they were doing things the U.S. government could not publicly admit to, like toppling unfriendly regimes; hence the "disavowed" if they were caught. In 2, 3, and 4, the threats are things like biological or nuclear weapons, and there's no reason for the U.S. to deny its interest in stopping them; you could send in a Navy SEAL team, kick ass, and then give a triumphant press conference once the mission's done. But in the first MI movie, the threat was that the identities of covert operatives would be revealed; that's bad, but it's also something the government would find deeply embarrassing. That's a perfect mission for the IMF.
What I liked about MI3 was that it was a big-budget episode of ALIAS, utilizing the strength of the series' premise without being constrained by the need to keep the story going on indefinitely. By including Ethan Hunt's personal life, it provided an emotional counterpart to the action and adventure. The similarity to ALIAS was almost too transparent if you had seen the series: opening with the climax and then flashing back; the protagonist hiding his occupation from his loved one, but then having his worlds collide disastrously; the technician back in the lab providing comic relief. But considering that ALIAS was more exciting than most spy movies at the time, following that template was a good idea.
Alas, I don't remember much about MI2.