Sorry of someone has mentioned this, but I highly recommend "Stories Of Your Life, and others " by Ted Chiang. Amazing writer with great versatility and a real tap on the human mind. Also find his story "Exhalation." Dunno where to find it in print but audio version can be gotten from Escape Pod (.org).
http://escapepod.org/2009/04/10/ep194-exhalation/

Also anything by Mike Resnick. But be prepared to get all weepy.

For military scifi, I say check out john ringo's posleen wars series, which starts with "A Hymn Before Battle." You can get it (and about a hundred other books) *totally free* at
http://www.baen.com/library/
From that same company, I would point out 1632, An Oblique Approach, and The Road to Damascus. That last one is one of my favorites because it makes you seriously wonder if a machine can have a soul.
Anyway, I'm typing from the back of a van on a 12+ hr trip and my thumbs are tired. Have fun.

Seems like we have read the same series and authors, LD. BTW, the Armageddon series is called 'Safehold' ... unofficially I think.

Mel, I can only wish a cat would adopt me. I made the mistake of not getting a cat before I got the corgis. They would have socialize and excepted one if I had. Now, they won't except one in the house.

If I had to recommend just one sci-fi book it would be Ender's Game. Orson Scott Card is a very skilled writer and Ender's Game is the pinnacle of his work. For a story written around a space war this books works surprisingly well for just about everybody (even my wife, who normally stays well away form anything sci-fi recommends this one).

David Brin, as you've already discovered, spins a good tale. Personally I enjoyed his uplift series the best, and found his subsequent stories too light for my taste.

David Weber's books are good adventure yarns. As someone already mentioned, Hornblower in space, what more do you need. His series with John Ringo (starting with March Up Country) is great if you have an interest in historical weaponry (stranded space marines teach primitive locals progressively more sophisticated weapons and tactics as they cross a hostile world).

Iain M Banks is probably my overall favorite (note the 'M' in the name: this denotes his sci-fi writing, though there are some sci-fi elements in several of his other novels). He's another skilled writer, with well developed story arcs and inventive settings. As Zorg mentions, Player of Games is a great place to start for a gamer. Alternatively start with Consider Phlebas or Against a Dark Background if skirmishes and/or RPG'ing is more your style.

This list of is pretty good, although some of the older books are there more for their classic/historical value, some of the more popular names (e.g. David Weber) and some other notable historical sci-fi authors (e.g. J.G.Ballard) are not represented.

(p.s. I too enjoyed Canticle for Leibowitz. The Darftstellar didn't grab me the same way, but Canticle is definitely a great work.)

Lord Valentine's Castle by Robert Silverberg. All the Majipoor series is pretty good. In fact, most (not all) of Silverberg's books are pretty good Sci-Fi. I can't believe no one mentioned Silverberg.

Roger Zelazny's Alien Speedway series by Jeffry Carver is good, too.

And if you humorous quandary type Sci-fi, try the Castle Perilous series by John DeChancie.

And if you like a mix of weird fantasy about RPGs, try reading the Gamearth trilogy by Kevin J Anderson.

Maybe someone can help me remember the title of this book:
A role-playing group is introduced to some lead miniatures that suddenly sucks one of the players into the actual world as his character. He wakes up with a bronze bracelet on that has ornamentation that looks like the facets of dice. He runs into several other characters with the same bracelet and they find out that whenever something important is about to happen, the bracelets come to life and "roll" their dice. Anyway, they figure out what it is that is that brought them to this world and go off in search of it.

It's a pretty old book. I found it at a library auction, kept it for several years and then lost it. I'd like to find another copy for my present library.

Humm... seems along time ago I read a series that was part scifi and part fantasy.

Piers Anthony "The Blue Adept" I think the name may have been. There is also a trilogy by Allan Dean Foster called "The light years beneath my feet" or something like that. I found it quite entertaining.