Startup: Julie’s alter ego from The Maxx saying "You shouldn’t be here, this is too private a place.
Critical Stop: Voice from the Springfield Nuclear Power Plant saying “Core meltdown in ten seconds…”
New Mail: Blue’s Clues song, “We Just Got A Letter!”
Shutdown: Krusty the Klown saying “Eh, I could pull a better cartoon out of my aaaa… hey! Whoah! Wasn’t that great, kid?”
Both my start-up and shut-down sounds are clips from the Hitchhiker’s Guide to the Galaxy (mini-series, I guess? Never seen it, just ran across clips online).
Start up: “In the beginning, the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.”
Shut down: “And so the Universe ended.”
AOL Instant Messenger:
Buddy sign on: “A chat with you and somehow death loses its sting.” (from Blackadder)
Buddy sign off: “I’m chanting as we speak. Bye-bye, darling.” (from Absolutely Fabulous)
Other than those, I have no special sounds set up. I also turn off as many as I can. They annoy me.
For a while, my PC at work played “Run for your lives! Run for your lives!!” (The Brain, as in Pinky and The Brain)
Didn’t last too long as a nearby neighbor expressed vague feelings of dread after hearing it.
Several PCs ago, back in the stone ages when Sound Blaster cards were THE hot new thing to have, and sound-related crashes were not uncommon, I had an explosion as an error sound. Anyway, one day, the error is triggered, and the Kablaammm! noise plays. During playback, the computer hangs and loops on that playback.
“KablaaKablaaKablaaKablaaKablaaKablaaKablaaKablaa…”
Naturally, I wasn’t even in the same room as the thing at the time, and the the windows were open. The neighbors were curious what all the racket was about.
Maximize window: “You are a meathead.” Archie Bunker
Download complete: “Hey, hey hey!” Fat Albert
Startup: the 5-second Ming Tea interlude from “Austin Powers: International Man of Mystery”
Everything else’s just factory installed.
Happy
This will drive everyone at work totally INSANE !! Love it!
Complaints are coming in already just from the first listen. If I never post again, they’ve killed me…
Startup: Elmer Fudd "Saaaaaaayyyyy, there’s something awfuwwwy scwewy going on awound heah!
Mail: classic Adams Family: (Whooop Whooop Whooop)(Morticia) Mail’s here.
Shutdown: The ending theme to Rocky and Bullwinkle
Exclamation; The obligatory “Doh!”
Critical stop: (Rocky) “This looks like real trouble, Bullwinkle”
(Bullwinkle) “Good. I hate that make-believe kind…”
I forget the rest, because that PC is at home right now.
I remembered another one. There’s a large frat-boy style belch whenever I empty the wastebasket.
Startup: The theme from ‘Simon and Simon’.
That would make an excellent sig line!
I’m a Veggie Tales fan. My computor used to boot with Archibald Asparagus saying, “Boot, you transisitorized tormentor! Boooot!”
Right now, sadly, it just boots to the default sound…
Well unfortunately the only thing my computer says to me is… you have preformed an illegal operation blah blah blah 
My mail checker spits out the MP & the Holy Grail clip where Cleese takes an arrow with a note on it…
<fssshhhwp> Mail for you, sah. [Collapses]
Other than that - not a peep.
My computer knows its place; it’s seen and not heard.
This wasn’t always the case. Many years ago, when I first had Windows 95 and MS Plus! (yes, ‘!’), I experimented with new themes. Like experimentation with mind-altering drugs, this had some lasting effects. See, my computer was an integral part of my stereo system at the time; I used it while recording tapes from one deck to another.
I still have a recording of some Enya album or other with subtle Winnie the Pooh quotes going in the background.
Due to multiple threats on my life & well being, I was forced to remove the Blue’s Clues mail .wav from Jophiel’s post
Took less than 1 day !! About 8 emails…
Well, my startup is the old 1980’s theme song for Tom Baker’s Dr. Who…
My defauly sound is ‘shit’ said very fast as to not offend anyone…kind of like sht…
Thats about it, I like the Gene Wilder “It’s Alive!!” good idea. !!
I have the system sounds turned off, so I don’t have anything like that.
However, my computer does often tell me to “spawn more overlords.”
Was that playings of the .wav or eight e-mailed death threats? 
Startup: “Hello … Smithers … You’re … quite … good … at … turning … me … on.”
(not really, unfortunately.)
Jess: high-five for "Buddy sign off: ‘I’m chanting as we speak. Bye-bye, darling.’ "
Startup on my Mac:
“Hey, Brain, what do you want to do tonight?”
“The same thing we do every night, Pinky: try to take over the world!”
And at shutdown:
“Pinky, are you pondering what I’m pondering?”
“I think so, but where will we find an open tattoo parlor at this time of night?”
(Both from Pinky and the Brain, if you didn’t figure it out. NARF!)