EIA reports ~1000 wells in Saudi Arabia.

So, yes - there's LOTS of room for "infill" and "extension" drilling to increase reserves, even in existing fields.  By comparison, the US has literally hundreds of thousands of wells.  To be sure, the vast majority were drilled more than 30 years ago when drilling was much more of a hit-or-miss affair, especially the tens of thousands of wells in Pennsylvania, Ohio, and Texas drilled before 1950.  Michigan, for example, allegedly has over 40,000 wells!

I think the reason for this is the extremely high permeability of the big Saudi carbonate reservoirs (such as North Ghawar). So their wells produced unheard of volumes of oil flow compared to the rest of the world, but it also takes fewer wells to drain the thing. That's also why their costs of production were so low historically. However, the smaller fields, and South Ghawar which is apparently much less permeable, may benefit from more wells. There are interesting numbers on Ghawar permeability here. However it's apparently an extremely inhomogeneous reservoir even locally (which is what has kept their technical people busy as water breaks through to the oil wells on the channels of high permeability.

It's a good deal more than 1000 (although try to find an exact number on the internet - good challenge).  The most recent I have come up with is 1430 producing wells in 2001
( http://www.unitedstatesaction.com/eia-june-2001-oil.htm ), although this seems a bit low since Chevron (operates in the neutral zone between Saudi Arabia and Kuwait) has 779 production wells online there alone (google chevron neutral zone).   Also, note that this source suggests 3400 have been drilled into Ghawar alone ( http://home.entouch.net/dmd/ghawar.htm ), although some of those have been converted into water injection wells undoubtably.   ARAMCO publications state the number drilled "in the thousands" ( http://www.saudiaramcoworld.com/issue/198803/well.done.well.seven.htm )

Of more interest, perhaps is the number of wells drilled per year.  The same article states 246 drilled in 2001, 292 drilled in 2002, to 325 in 2004.  Note that the last number was the beginning of the year projection - the annual report has 260 actually completed, so I have no idea if their dry hole rate is 25% or if those wells were never drilled.   Note that they recently signed contracts with 5 off-shore rigs, outbidding ultra-high rates in the Gulf of Mexico.  Given those numbers, and an inferred decline of 800,000 bbls/d, new well rates at best are probably in the 2000 barrel/d range.  Given that ARAMCO was boasting about a 3300 bbl/d light oil discovery in the press ( http://www.adnki.com/index_2Level.php?cat=Business&loid=8.0.165089657&par=0 ), I am of the opinion that not everything in SA smells like roses on the drilling front.  For example, from early 2004, the claim was that production would increase by 1.1 million barrels by the end of the year ( http://www.washingtonpost.com/wp-adv/specialsales/spotlight/saudi/art4.html ), but exports have been stuck at 9.5 million barrels per day.  In my view, 2005 should be a landmark year - if they have 90 rigs working and can't produce more, the writing is on the wall...

OPEC just released their Annual Statistics Bulletin 2004. In there you can find numbers for completed wells, running rigs and producing wells 2000-2004. I was just compiling the data this evening!

Here's the interesting stuff (pags 47-50 from the pdf, 3,73MB):

OPEP

Active Rigs
2000 253
2001 281
2002 243
2003 229
2004 272

Wells Completed
2000 2805
2001 2542
2002 2905
2003 2827
2004 2579

Producing Wells
2000 35719
2001 35659
2002 33454
2003 32315
2004 33580

Saudi Arabia (Saudi-Kuwaiti Neutral Zone not included)

Active Rigs
2000 27
2001 32
2002 33
2003 31
2004 34

Wells Completed
2000 257
2001 265
2002 250
2003 330
2004 335

Producing Wells
2000 1550
2001 1575
2002 1525
2003 1780
2004 1757