How can we play a shorter but satisfying game of Arkham Horror?
3-4 hours is good.  8 is way too long!  

Without seeing you play it's hard to say with precision where your time is being spent inefficiently, I do have a couple suggestions though.

Setup efficiently

Setup can be done in 5-10 minutes but can easily drag on for half an hour.

Setting up is a job for several people.  The most experienced person should be handing out tasks like:


Shuffle the Mythos deck
Get clue tokens on every space with this red diamond on it
Hand out character cards to everyone, figure out what fixed items are needed and search for them.
etc


Play Cooperatively

My group got a lot more efficient when we started talking before we moved.  A simple 30 second discussion of what each player's plans are for that turn can end up saving a lot of time.  For example: I found that big stalls happened when the 2nd player to move took the clue tokens I was aiming for.  With a brief chat, that sort of conflict can be hammered out.

This also allows an opportunity for someone to mention that they really can't do much unless someone else kills that pesky Dark Young hanging out in the streets.

Upkeep as well as Encounters (Arkham or Offworld) can generally be done simultaneously.  However my group prefers that all encounter cards be read aloud so the whole group can enjoy them.  The shuffling and drawing is done ahead of time so there isn't much waiting though.

Job 1 - Closing Gates

Arkham Horror is a great game, dripping in style.  It is a lot of fun to have encounters, kill monsters and collect a lot of items and spells.

The game plays a lot faster if you keep closing gates as job 1.  With 5 players several people should be tasked with collecting clues and hopping off world as quickly as possible to close the first couple gates.

Injury and Madness

The Dunwich Horror expansion added Injury and Madness cards.  These cards greatly change what happens when an investigator loses all of her sanity or stamina.

Under the original rules losing all of your sanity or stamina causes


loss of half your items
loss of half your clue tokens
reset the sanity or stamina to 1


With the Injury and Madness rules


No loss of items
No loss of clue tokens
reset sanity/stamina to maximum
Gain an injury or madness card


Either way you move to Saint Mary's Hospital or the Arkham Asylum as appropriate.

Whether or not you own Dunwich Horror, I would encourage you to use these rules.  The original rules are too harsh and potentially cost the player many turns to regain the lost items/clues/stamina/sanity and results in a slower game while the player recoups.

If you don't have the cards, just ignore them.  Or pick a couple that sound cool off of the Arkham Horror Wiki and make your own custom chart and roll a die to get a result.

The Great Old One equals Game Over

If our game is running long, we declare that we have lost if the Great Old One shows up.  In the first edition of the game (late 80's) this was the rule.  Fantasy Flight adjusted it when they remade the game.

This can depend a lot on the GOO as well.  Some of them, particularly in the base set, make for long combats.  They neither kill the investigators very fast or have the decency to die quickly themselves.

You can easily just skip all that and stay true to the the Chthulu Mythos by admitting that the world is lost when the GOO shows up.

Note - if you follow Job 1(noted above), you'll be seeing a lot less of the Great Old Ones!