I thought Halo 3 was too full of next-gen gamin cliches.
I.E. Covering up bad repetitive game design with beautiful graphics and completely ruining the immersion for me by adding that stupid helmet overlay and still not including a static health bar or any sort of health bar at all. Halo 3 was decent, but it was by far the worst in the entire series. I'd pick Halo Wars over Halo 3. Halo: CE was by far the best, as it included the health bar underneath the shield, implementing the perfect blend of tactical battlefield strategy and FPS survival.
Halos 2 and 3 don't need a health bar, because it regenerates like shields though slightly slower. Master Chief upgraded to MJOLNIR Mk. VI armor at the beginning of Halo 2, which has built-in biofoam injectors.
Bungie hid it so they could put in all these convoluted mechanics. It only starts to regenerate after a certain amount of time out of combat, etc. You shouldn't need to see it, because if your shields are gone you should be ducking into a hidey hole. Not to mention it's a much less brutal system... the health system of Halo:CE was what made Legendary nigh impossible sometimes.
Halo Wars was a terrible excuse for an RTS in my opinion. It comes down to building a massive army of tanks, the Flood are terribly unbalanced and unplayable, and it's riddled with inconsistencies to the rest of the Halo series. (Elites with claws? Grunt/jackal combat forms?) But nitpicking aside, I'm probably just spoiled by computer RTS games like C&C and Starcraft.

Anyway, Halo is less Bungie's baby than it is Microsoft's baby.
Microsoft bought Bungie after Halo was well in development. If you see gameplay footage from the 90s (it was announced in 1999 after it had been underway for several years; Bungie was bought in 2000) it's evident that Bungie's vision remained largely intact. The biggest differences were cosmetic (elites with one jaw, Master Chief with an antennae, smaller scorpion), aside from things that were cut due to constraints (some of which were added in Halo 2, such as the particle beam rifle and specter).
The Covenant, particularly the Elites, seem kind of noobish - what happened to Fall of Reach/Halo 1 elites and their kickassery? Their ability to challenge a Spartan one-on-one in hand-to-hand combat?
This could be said about the other games as well, though to a lesser degree. Eric Nylund was either taking a huge artistic liberty, or writing based entirely on Legendary.

Though I suppose if the John-117 of the books was able to blow away his enemies with the ease of a video game character, it would detract from his otherwise amazingly well-written story.
Give me Cortana any day.
Seconded. Halo would have been very quiet without her witty comments, too.

Though I think she was a much more interesting character in the books.
And as for my favorite levels... I'd have to say in Halo:CE it was either Truth & Rec or The Library. No, I'm not a masochist, The Library is just a huge challenge. And I like challenge. Though my favorite moment is the finale. And I always found Silent Cartographer to be rather annoying... I have no idea what all the love is about.

In Halo 2 I liked Cairo Station and that level after Outskirts. The one where you kill the scarab. It had good vehicle action.
In Halo 3 the only favorites I have are the part of The Covenant (I think that's the level) where you kill the scarab on foot, and the homage to Halo:CE's ending. The whole game was good but not great. I liked Halo:CE the best... it had a certain charm, probably because it wasn't trying at all to be balanced (is the pistol really a tiny rifle?

). Grenades were also very
overpowered fun in Halo:CE.