What is the force exerted by the catapult on aircraft carriers?
Takeoff

Steam/power settings are adjusted for each a/c type and T/O weight.

The EMALS stores 484 MJ in four 121 MJ alternators spinning at 6400 rpm. It delivers up to 122 MJ over 91 m. That averages out to 300,000 lbf. EMALS more finely controls launch forces (Max Peak-to-Mean Tow Force Ratio = 1.05), allowing it to launch smaller a/c (eg, smaller UAVs) and delivering a smoother ride that reduces airframe fatigue.

Current steam catapults deliver up to 95 MJ over 94 m. Each shot consumes up to 614 kg of steam piped from the reactor (NB: not the primary coolant loop). That averages out to 230,000 lbf.

Accelerations average around 3 g's, peak around 4 g's. 

Landing

Landings are stressful (notice the fuselage skin wrinkling beneath the radome on this Hawkeye): 


(Source: DoD photo by: PHAN KRISTOPHER WILSON, USN Date Shot: 11 Jan 2005.)

An F/A-18 touches down around 720 fpm (12 ft/s). It's rated to twice that. CTOL fighters typically do about half that. I believe airliners average under 200 fpm (3 ft/s).

Here an F/A-18 is dropped from 20ft (36 ft/s, 2200 fpm): 
                
            



Service life

NATO fighters are typically designed for 30 year service lives (6,000 to 8,000 flight hours). Historically, Soviet/Russian fighters fly much less. The Su-27SK is rated for 2,000 flight hours over 20 years. [See table for cost and service life comparison.] F/A-18's were built for 20 year service lives, 30 years with service life extensions.

The fuselage and landing gear are much stronger to withstand carrier landings and launches. The nose gear regularly transfers 4x the takeoff weight of the a/c into the rest of the fuselage. 

Compare the F-35A's CTOL nose gear:

(Source: USAF)

...to the F-35C's CATOBAR nose gear:

(Source: USN)



Here's an excerpt from a Naval Air Warfare Center paper on EMALS:


  Other drawbacks to the steam catapult include a high volume of 1133 m3
  , and a weight of 486 metric tons. Most of this is top-side weight
  that adversely impacts the ship's stability and righting moment. The
  large volume allocated to the steam catapult occupies "prime" real
  estate on the carrier. The steam catapults are also highly maintenance
  intensive, inefficient (4-6%), and their availability is low. Another
  major disadvantage is the present operational energy limit of the
  steam catapult, approximately 95 MJ. The need for higher payload
  energies will push the steam catapult to be a bigger, bulkier, and
  more complex system.

Endspeed:      28-103 m/s [54-200 knots]
Cycle time:    45 seconds
Weight       &lt; 225,000 kg
Volume       &lt; 425 m 3

  
  At max speed, the output of one of the disk alternators would be 81.6
  MW into a matched load... These magnets have a residual induction of
  1.05 T at 40 oC and create an average working air gap flux density of 0.976 T, with tooth flux densities approaching 1.7 T... Maximum output voltage is 1700 V (L-L) peak and current is 6400 A peak per phase. The
  disk alternator's overall efficiency is 89.3%, with total losses of
  127 KW per alternator. This heat transfers out of the disk alternator
  through a cold plate on the outside of each stator. The coolant is a
  WEG mixture with a flow rate of 151 liters/minute. The average
  temperature of the copper is 84oC, while the back iron temperature is
  61oC.




Sources:


EMALS/ AAG: Electro-Magnetic Launch &amp; Recovery for Carriers
Electromagnetic Aircraft Launch System - EMALS
Steam catapult types
Electromagnetic Aircraft Launch System - EMALS - NAWC