How much speed can I buy I am currently riding an entry level carbon road bike (Fuji Gran Fondo 2.5, compact 50/34 crankset, 105 group, 12/30 10 speed, Oval 327 wheels, but I suspect the details are not important-you have all seen similar bikes on club rides)  My typical ride is 30 miles and 1500 feet of climbing (as reported by Strava, if I add up the hills they are not this high) in 2 hours, so I am not a speed burner.  The Gran Fondo is promoted as an "old guy's" (which I am) bike-the head tube is a bit longer (only 1/2 inch) than standard so you sit more upright, you get (my year, not now) the 30 tooth on the rear and the tires are 25 instead of 23.  Will another bike blow me away if I ride it a short distance (5 miles) on the flat?  How much time can I save at the same power input over the 30 mile ride? Let's pretend I have no budget limitation, I just want the fastest (easily available commercially) road bike for my use.  How much faster is it than what I have?  What would you look for? Don't send me looking for an 11 tooth on the cassette-I rarely use the 50/12.  You need to send me to a class descending hills faster first.  

Added based on Craig Hicks answer:
I have inverted the stem, which probably counteracts the longer head tube of the bike I have.  I didn't notice any difference in comfort.  I could take a couple spacers out of the the head tube to lower the bars another inch.  I did a high end fit with my LBS with some comfort improvement but no speed.  I suspect the biggest speed increase I could buy would be race tires that have less rubber so less flexure loss on the road at a price of durability.  That is what I was looking for, what should I look for and how much would it speed me up?
A bicycle in and of itself is a half of the equation.  If you want to eek out as much speed as you can you also need to consider how you interact with the machine.  This answer focuses on the human/bike interaction rather tweaking bike specs.

Bike fit is a continual compromise between power, comfort, and aerodynamics (Bike Fit by Phil Burke). Simply plugging specs into a worksheet will not give you insight into these types of compromises.  New high-end bikes can be problematic as they are often very aggressive.  As you get older if you compromise the comfort dimension too much your power can drop of substantially.  You may be more aerodynamic, but you can end up slower due to a drop in sustainable power! 

Flat Land Speed

In terms of absolute speed on flat cutting down your frontal area (i.e., aerodynamic drag) will go a long way to increasing your speed. There are lots of little tweaks you can do to your current setup if it is currently fitting you well.


Tighter fitting clothing (any flapping clothing = aerodynamic resistance).
TT bars are another big aerodynamic gain (don't use on a group ride though).
Supple fast rolling tires pumped to the appropriate pressure.  (This isn't always the max pressure and can change from tire-to-tire.  You really need to experiment here)
Tweaking your current position to further optimize the aero/power/comfort relationship.
Drive train gearing


Tighter  gearing ratios (aka a smaller range in the rear cassette). This can let you fine tune your cadence more.
Big/big combinations are more efficient that Big/small gearing combinations for a given chain line.

Maintaining your drive train!


Climbing

Here a lighter bike will help, but also more appropriate gearing is very important (aka low enough to spin up all the climbs).  As Andy256 suggested you an play with some calculators.  But again I will harp on bike fit. Do you have the hand positions available to put you in a open upright climbing position so you can breath properly? Are your shoulders, neck and back relaxed on climbs.  Do you have enough hand positions (i.e.,drops) so that you can comfortably get in the drops on decent and faster sections.

Going up to get down

One day I finally admitted to myself that I could not ride the slammed positions of my youth and revised my cockpit putting myself in a more upright position.  The result of this is that I am much more comfortable on the hoods and can crank out the climbs at a harder pace.  I can also use my drops a lot more now as the higher hood position this give my back a change of position it now needs. My drop position is still quite aerodynamic position and I can spend a lot more time in the drop position than I have been able to in the past.  Overall I don't think my aerodynamics has been too adversely affected as I am using the drops a lot more than even when I was younger (then I used to just use them in crits, sprints and pursuits).  I wish I had taken more measurements when I was younger to confirm or refute this thought.

I suggest taking time to investigate how bike your current fit compliments your bio-mechanics before delving into the quest for new gear.  You might be surprised how many gains you can find!