The brakes are much more effective than anything else, at least for the jet I have experience in (EMB-145).
Our landing performance data typically assumes full braking application, spoilers deployed and no reverse thrust.
The airplane will most certainly stop without using reverse thrust, just not as fast.
I never tried not using the brakes, and if I were to I would want a light airplane and a very long runway.
As Lnafziger pointed out in the comments, the brakes are part of redundant systems so that they are always available.
In the EMB-145, the brakes were serviced by two independent* hydraulic systems.
The inboard brakes were on one system while the outboards were on the other for a total of four wheels each with big carbon fiber brakes.
To address the comments on slick runways, assuming braking action allows an attempt to land in the first place, you have to be careful.
With reverse thrust alone you may not be able to maintain the runway centerline and directional control may become difficult through uneven deployment of the reversers and other factors.
In this scenario the spoilers are helpful to increase traction and brake effectiveness.
In short, if the runway is slick then the only way I'm attempting a no-wheel-brake landing is after declaring an emergency.
Finally, to address the question in the title, the wheel brakes are always the primary means of slowing the airplane.
*
You could transfer fluid between our systems through the parking brake.
aviation.stackexchange.com/users/258/casey
Perhaps instead of thinking of a single primary means of slowing a large jet, we should think about a primary means for a given set of conditions, the combinations of which are numerous.
To mention a few: What is the weight of the aircraft.
Passenger aircraft are typically nowhere near max landing weight when they land.
Freighters are often loaded such that they may be very close (or even over truth be told) to max landing weight.
Is the aircraft going to be on the ground a sufficient time for brakes heated to their max to cool?
Was the leg from which you are landing long enough to allow the brake and tire energy from the taxi and takeoff to dissipate?
Is where you're landing used to having to handle hot brakes and thus can be expected to have a huffer readily available to cool them and people who know how to do it?
Do you have a reverser locked out for maintenance.
Does your next departure allow for safely leaving the gear down for awhile and thus gave you more leeway on heating the brakes when you landed.
Just some thoughts.
aviation.stackexchange.com/users/394/Terry
This video on YouTube shows a 777 in certification trials, accelerating at maximum gross weight from standing start to $V_R$, then stopping with maximum brake pressure and no reverse thrust.
The brake discs are also ground down to the minimum thickness permitted by the maintenance manual to simulate the worst case scenario.
The brakes get white hot!
Then the plane has to taxi for 5 minutes, before having the fire department cool the brakes.
The test is to ensure that the brakes can handle the maximum load as certified, and secondly that the brakes do not catch on fire and incinerate the airplane.
If the runway is slick it just takes longer to stop.
Thrust reverse will help significantly in this case.
Thrust reverse is prohibited below a certain speed because the reverse thrust will kick up FOD which the engines may suck in, causing expen$ive damage.
However, in an emergency, thrust reverse will stop the plane.
aviation.stackexchange.com/users/291/Skip Miller
While landing you want to reduce speed for which you need spoilers and to have more lift and drag
you have the Flaps deployed than just when you touch down on runway ground spoilers are deployed.
If want to land with short runway length then you go for reverse thrust (nice to have in normal scenario but
in case of emergency it can be a life-saver).
Then we need wheel brakes to stop the plane.
Effectiveness: When in air/near ground: only spoilers/Flaps and airbrake (ground spoilers) are effective to reduce speed of aircraft but not to stop it
Flap are required to keep the aircraft in a configuration such that you don't crash on ground When on ground: you still have airbrakes/spoilers effective when aircraft speed is high but its effectiveness decreases at low speed.
So, are other control surfaces useless @ low speed (Flaps/Spoilers etc).
Reverse thrust and wheel brakes are the one you can rely on.
Failures:All critical systems on aircraft have redundancy so the probabilty of failure is around 1e-8 /flight
-hr
but still you never know.
I think you will be able to land
but you need more runway length in case of two fail scenario.
Yes, I believe you can land without wheel brakes by using reverse thrust but purpose of reverse thrust is only to reduce aircraft speed such that we land on short runway.
so, its not recommended to not use wheel brakes and use reverse thrust.
Slick runway/rain or snow on runway has same effect as it has on other land vehicles..
Aircraft will take more runway length than usual.
aviation.stackexchange.com/users/685/ToUsIf
plain and simple: the brakes.
Reverse thrust is much less effective than brakes.
And that's just talking about the force to slow down, not even taking into account that jet engines need a few seconds to spool up (6 or more) and brakes are effective immediately (perhaps 1 s delay).
aviation.stackexchange.com/users/9483/Andreas Lauschke
I understand that a large(r) commercial jet slows down after landing using the following methods:   Wheel brakes  Reverse thrust  Spoilers/flaps/airbrakes   What is the effectiveness of each compared to the others? What if one of the first 2 fails? Can an airliner usually be stopped without using wheel brakes or without using reverse thrust?  And what if the runway is slick because of rain, snow or ice? Does that change the equation?
For large jets, what is the primary means of slowing down after landing?
aviation.stackexchange.com
<landing><airliner><braking><thrust-reverser>
aviation.stackexchange.com/questions/1219
aviation.stackexchange.com/users/4/Philippe Leybaert
The brakes are more effective than anything else. Our landing performance data typically assumes full braking application, spoilers deployed and no reverse thrust.   While reverse thrust and spoilers deployed do help to slow the plan down, it is the brakes that do the most work.
Users suggest the brakes play the most important part Thrust reverse also helps.