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...