Luca Brasi.

During the beginning of part 1, when Don Corleone is meeting with people, Tom Hagen says that Luca Brasi is here to see him, and he wasnt expecting to be invited. Don Corleone asks is it necessary, why was the Godfather hesistating to see him?

Also, whats Brasis' background- was he just a soilder? What are his connection with the family?

Weran, this is a prime example of how the novel adds detail that could--should--have helped us in the film:
Luca was a very special case in Vito's background. Without revealing too much (in case you want to read the novel, which would be well worth your while), Vito was asked to intervene with Luca by a woman who brought her woes to him. Vito found Luca a strange and savage man--and quickly concluded that he could put Luca's savagery to good use by making him his top enforcer. Luca apparently didn't have a regime of his own, but he reported directly to Vito--he didn't even go through Hagen. "Luca Brasi could do a job of murder all by himself," as the novel says, and could do it in vicious, even sadistic, ways that would scare Vito's enemies. I won't say more about that because you'll enjoy reading it.
The reason Vito seemed nervous was that Luca made him nervous: "He was like a natural force, not truly subject to human control" (or something to that effect). But, as you saw in the film, Vito called him "my most valued friend."

Thank you for clearing that up. Yeah im planning on starting on the novel soon, from what i hear its really worth the read.

Something I've always found curious is Tom's comment to Vito at the wedding about Luca "not expecting to be invited."

According to the novel, Luca was "one of the great blocks that supported the Don's power structure", so if I were Luca I would've expected to have been invited.

I hate to say this, but I think that Luca suffered from low self-esteem.

Plaw, I think that Vito took great pains to separate that side of his life from his family. Although Luca Brasi was very important to the Family, he represented the side of the business that Vito kept from his family. I think that the Don immensely disliked Luca and all that he represented, but saw him as a necessary evil, and important to his success.

All true, but Tessio and Clemenza were invited, as well as Barzini and that whole crowd.....

I think mustachepete hit it on the head (Luca may have had a low opinion of himself).

The book goes into how Luca CHOSE to idolize Vito.

Plaw, what you say is true about Clemenza and Tessio, but they were the Don's friends from when the kids were babies. Obviously they had a different relationship with the family than Luca did. Luca's sole occupation was one of violence. Although the caporegime's were violent men, that was not their only talent. It may be a thin line, but it's there all the same.

Yes, SC, as Turnbull pointed out earlier, the book goes into much more detail about Luca, how he came to work for Vito, and what kind of man he was. I know that some things had to be sacrificed in order to keep the movie to a realistic viewing time, but it's a back-story that was fascinating and added so much to Luca's character. In the movie, we only hear about the bandleader, which isn't a very scary story (except maybe to Kay), so why do the others seem so in awe of Luca? I think you really have to read the novel to find out.

I don't know about you, but I'be been scared to death of every guy named "Luca Brasi" I've ever known. And some of them were florists....

plaw, I'm guessing that Luca didn't expect to be invited because of his fearsome appearance and reputation--he might scare the other guests or detract from the occasion. Recall that when Joey Zasa and The Ant show up at Michael's party in III, the whole place goes silent.

"Low self esteem" could well be the reason. In the novel, in a scene that we're familiar with, he says that he doesn't want another person like himself to live.