Connie's wedding at the beginning of The Godfather was a huge event with hundreds of guests, even heads of rival families such as Don Barzini. Why then would Luca Brazi not expect to be invited?

(Tom tells Vito that Luca didn't expect to be invited and that he wants to see Vito to pay his respects).

I think because Luca didn't think he was important enough to be invited to the wedding of the Don's daughter. The idea being that he's just the Don's enforcer and wouldn't rank high enough to be invited to a social event. By being invited it shows that Don Corleone respects Luca's "talent" and considers him "[his] most valued friend".

Perhaps Luca felt that as an employee of Don Vito, however closely they valued each other as friends...he'd have no place at the wedding of the Don's daughter.

After all, Luca was not Don Barzini. He may have felt uncomfortable among the hundreds of relatives and more prominent guests. For we know, it may have come as a surprise to Luca that Paulie was invited as well!

Perhaps the novel provides more insight as to Luca's feelings on being a guest at Connie's wedding.

Apple

Another possibility is that, in addition to being an employee, Luca recognized that he was a big, scary thug and might make the Don's guests uncomfortable. By inviting him, the Don pulled off another of his patented loyalty-enhancing moves by earning even more gratitude from Luca.
Apple: I had the impression that Paulie was mainly pulling guard duty at the wedding (Clemenza to Paulie: "What are you--a dance judge? Take a walk around the neighborhood: do your job").

Me too.

I'm thinking of it though in terms of how Luca may have interpreted Paulie's presence.

Still though, you're right. Luca might have realized (if he cared) that Paulie was there to work and he was simply an invited guest...after all, one is probably not called upon to whack someone during the wedding of the Don's kid, and that was Luca's primary role in the Corleone family!!

Apple

I also think that Luca accepted his position as part of the darker side of Vito's life. It was a part of Vito's life that he didn't necessarily want out in the open. I think that Luca was what we would term "a necessary evil" and was used to being more secretive about his role in Vito's family. I agree with TB (shocking, I know) that be inviting Luca to be a guest, by referring to him as a friend, Vito cemented Luca's loyalty even further.

However by doing this...Vito makes it even more unfeasible months later for Luca to convince Sollozzo/Barzini that he is 'unhappy' with the family. He should've known that it could never work.

If your theory (and agreement) of why Luca was invited to Connie's wedding is correct, then Vito pretty much signed a death warrant for his 'most loyal and trusted friend'.

Apple

Indeed he did. It was a shocking lapse of judgment on the Don's part to assume that Sollozzo and Tattaglia would believe that Luca would betray the Don--or even simply "leave" the Corleone Family to "work" in their operation. Another example of why the Don, "rest in peace, was slippin'."