This is what we want it to look like when we are done...

It's a function of your beams and joists. The thicker they are, the more you can span between posts. Linked below is an excellent deck construction guide. In the first few pages are span tables that you can use to figure out how to minimize posts.

Decks.com is also a good resource. For $200 (when I built mine it was only $100), they'll do your structural design for you, and spit out a materials list. You can specify that you want to minimize posts. I was very happy with their product and turnaround time (a couple days).

Here is a link that might be useful: AWC's Deck Construction Guide

I understand the relationship between beam and joist size and post spacing.

I will post some pictures that might help clarify what I am asking.

I don't know how to post multiple picture in one post, so I have to respond three times.

The picture below is what it would look like if I was building a 32 x 34 deck with all 2x12 beams and joists.

Since there are walls on both the left and right, there are several problems created by the post footers marked in yellow.

It seems like I should be able to work around it by using the ledger boards on the left and right.

If I did something like the below picture, each area (light green, light yellow and light blue) would be like its own separate deck.

The problem area is the dark blue corners. Not sure what I should do there.

I don't think you are allowed to cantilever beams any more.

How do I get around not having post footers next to the house?

Is it acceptable to "hang" a beam off the perpendicular ledger board. Is that equivalent to a post being there?

Your diagrams help clear up your question a lot. Thanks. BTW, to post multiple photos in one post, you have to load them into a service like photobucket, and then you paste the HTML code from photobucket into the body of your GW post.

So basically, you want to cantilever your beams off your posts, or else support them with the ledger board.
Page 5 of the guide I linked above says "Deck beams can extend past the post centerline up to LB/4." So if you've got an 8' span, you can cantilever it 2'. If you went with triple 2x12 beams, they can be supported on posts 10'-8" apart, so you reduce your footings from 5 to 4 per beam, and they are up to 2'-7" away from the house. Does that solve your issue?

I have not heard of supporting beams on ledger boards, and to my engineer wannabe brain, that doesn't seem sufficient for support. But perhaps a pro or actual engineer will pipe up with some more data on this.