[Updated October 23, 2006] According to Dr. T. S. Kelso at CelesTrak WWW, if you visit a website called the SATCAT Boxscore you will find pretty much everything we know orbiting the earth as of today greater than 10cm in size.
In summary: there are about 3,100 satellites "on orbit" but only about 1,000 are still active (it is very difficult to determine the operational status of a satellite). Another 2,700 are labelled "decayed payloads" which means they are no longer on orbit. Most have experienced uncontrolled reentry and burned up, but some, such as the space shuttle, are actually controlled reentries. There are only 10,036 objects--payloads or debris--which are still in orbit of the 29,496 placed in orbit to date.
The boxscore includes all satellites launched into orbit, even US military satellites. Of course, there is no orbital information available to the public on military satellites. By way of comparison, the data released by NORAD today (Oct 2006) has 2,752 payloads and a total of 9,010 objects. Contrast this to the 3,118 payloads and 10,036 objects currently in orbit in the SATCAT. Most of these 'missing' satellites are US Department of Defense satellites (restricted and classified) but some are interplanetary missions which do not have Earth orbital information.
According to Wayne G. Winston, Direct Readout Coordinator, NOAA/NESDIS, regarding weather satellites, "There are many in orbit but no longer working. They have either failed, or were purposely turned off to make room for newer satellites. So I'll confine the answer to those that are actually transmitting useful data, most of the time.
U.S. - 6 (civilian), 4 (US Air Force)
Europe/EUMETSAT Consortium - 2
Russia - 2
Japan - 1
India - 1
China - 2
Canada also has Radarsat, used for various aspects of remote sensing, but not particularly meteorology -- the closest related field it sees a lot of use is for ice mapping over the Arctic/Antarctic because of its ability to see through clouds. In fact, the broad category of "remote sensing" easily includes more than 100 satellites. For meteorology, Canada uses the U.S. NOAA (National Ocean and Atmospheric Administration) satellites, and has no meteorological satellites of its own.
This gets into a side issue of meteorological satellites. Since the U.S. launched the first weather satellite (April 1, 1960), our policy has been that of open and free use by all, without any restriction (the civilian satellites, not the Air Force sats), and most of the world has followed this policy. Only India encrypts all of their, and Eumetsat most of their meteorological satellite transmissions. This open use policy means most countries do not need to launch their own weather satellites."
To answer your final question, as far as I can tell, the maximum number of satellites is infinite.
A computer program called FreeFall tracks up to 1024 satellites on your screen. Visit Advanced Analytics.
A computer program for Windows can track about 20,000; Orbitron.
The most comprehensive catalogue of satellites is available at CelesTrak. Here they have mathematical orbital tracking data (known as TLEs "Two-Line Elements") numbering 83,207,332 TLEs. Most of these are historical since each satellite will have a new TLE produced every couple of days.
Reader William Lockie asks: What is the protocol used to determine where each country is allowed to put its satellites to avoid using the same location in space. The name of the list please and who controls it?
Astronomer, Don Barry replies:
Historically, there has been very limited regulation in this area -- though from the very beginning of man's use of near-earth space, attempts to coordinate knowledge were begun through the International Committee on Space Research (COSPAR) which is part of the non-governmental International Council of Scientific Unions.
Quite recently, the International Telecommunication Union (ITU), which is recognized to various degrees by different governments, has begun coordinating the allocation of usable sites in geosynchronous orbit. The only area not so organized on a recognized basis by them is the slice covering the Americas. The ITU arm so responsible is the World Administrative Radio Conference (WARC). You can find a number of search-engine results containing minutes of their meetings, which occur every 2 or 3 years.
Fortunately it is very unlikely that satellites themselves will collide-- though this has happened. The greater potential problem is that the radio frequency bands available in the beamwidth of a satellite's antenna get quickly filled, and no more communications bandwidth is available to ground stations using these satellites. Since the only area of near earth space which presents the same "fixed" orientation of the satellites to the ground is geosynchronous orbit, this is the primary area that has a problem.
There *is* the problem of increasing density of satellites, mainly dead satellites, in near earth orbit. In particular, several upper stage booster rockets have exploded, creating not just one relic, but thousands. It is conceivable that at some point a cascade of collisions could reduce much of low earth orbit space into a debris field and render this area useless to satellites. The primary launching governments have started practicing some degree of good stewardship in this area, making sure that booster rockets deorbit or at the very least vent fuel which could cause explosions after they've performed their function. Paint has also been a problem -- a 1/4" pockmark on a space shuttle windshield some years back was traced to a small fleck of paint from the upper stage of a NASA booster.
However, American hegemony in this area has led to a more or less "we set the rules" approach, especially in recent years. Nuclearization of near earth space, which was abandoned after several accidents in the 70's, culminating in the reentry and contamination of parts of Ontario in 1979 by a Russian spacecraft with onboard nuclear reactor, may soon resume. American military interests, in the guise of promoting "scientific research", would like to see development of high power space-qualified reactors. They claim these would be used in exploration missions to the outer solar system (such as a proposed mission to orbit several of the moons of the planet Jupiter), but it is generally believed that this is merely a cover for development of technology primarily intended to provide the capability to destroy other satellites in Earth orbit on command, should the perceived military need arise.