If you are asking one of each type on the bike, yes.
As disc brakes were becoming popular, many companies produces bikes with a disc in the front and a rim brake in the rear.
If you are asking about one of each type on a single wheel (three or four brakes total for the bike)
yes that would also be possible, but there wouldn't really be a point.
Also common during the industry's transition from rim to disc brakes where frames that were designed for either.
Bikes on a manufacturer's less expensive spectrum would have rim brakes and for a few hundred more, the same frame could be had with disc brakes and perhaps nicer components.
If one was to actually install a disc and rim brake on the same wheel, there would be some obstacles to overcome (assuming you wanted to actuate both brakes with the same lever).
To make the brakes grip roughly the same (ie not one just one doing the work and the other making no contact)
you'd have to make sure the actuation ratios or cable pull was the same for both brakes.
After that you'd need to use some sort of BMX style adapter to make sure both were being pulled by the same lever.
You'd also have to carefully adjust them to make sure they making contact at roughly the same time in the pull.
Finally you can expect that since disc pads and rim pads probably don't wear at the same rate, all the work would have to be redone often to keep the two working in unison.
All in all you'd be paying for twice as brake for a setup that would probably work less consistently than either brake alone and require much more maintenance than either alone.
If you were just wanting more stopping power, you could simply install a larger disc brake (AM or DH sized) and deal with much less setup.
EDIT:
I hadn't considered the possibility of a coaster + rim or disc.
Since a coaster brake would be actuated separately (by pressing back on the pedals)
it could be potentially more useful and much less tinkery to maintain.
That being said ANY brake should be able to lock up a wheel so it still won't gain you anything except a safety backup in the case of your primary brake (whichever you chose to use) failed.
TL;DR Possible, but not worth the effort.
bicycles.stackexchange.com/users/13710/Deleted User
It's not unusual for tandems to have three brakes, with a rim brake and disc or hub brake on the same wheel.
Traditionally they had a drum drag brake on the rear wheel for long descents, operated by the stoker, to avoid overheating the rims.
Some modern disc brakes are up to the same job, but many aren't, though this is a subject where opinions are varied.
http://www.thorncycles.co.uk/tandem-braking http://santanatandems.com/Techno/UnderstandingBraking.html
http://www.sheldonbrown.com/tandem-brakes.html http://www.tandems.co.uk/tandems-explained/
Tricycles often have both brakes on the front wheel, and that could be done with a disc and a rim brake.
UK law at least requires that bicycles (unlike tricycles) have braking systems on both wheels.
You could have two brakes operated by one lever (as is done for some disabled cyclists), but when one brake is enough to lock the wheel, I can't see any reason to do so.
(On an expedition tourer, having rim brakes fitted as a backup in case you can't get spares for a disc brake might make sense, but you would only use one at once on a given wheel.
Even then, you would probably just use a frame where rim brakes could be fitted if necessary.
Or just pick one .)
bicycles.stackexchange.com/users/1158/armb
When disc brakes first appeared - a lot of mountain bikes ran with a single disc brake (mechanical) at the front and a vee brake at the rear.
Whilst not ideal in terms of rear braking power or aesthetics - it's a perfectly viable option and might even make the task of fitting panniers to the rear of a bike easier.
bicycles.stackexchange.com/users/16979/OraNob
There would be little point to put both kinds of brakes on same wheel.
No matter how hard you brake, the maximum amount of force you can apply is just before when the wheel locks.
Add any more force and the wheel locks, add even more
and it just keeps on being locked.
Either type of brake alone is perfectly capable of locking the wheel under normal circumstances, so there is little point to try to add any more braking force.
bicycles.stackexchange.com/users/31794/tylisirn
See the Merida Komfort model for rent at Finse 1222 .
They offer a bike with front and rear disc brakes, plus coaster (pedal) brakes.
These are used on the Rallarvegen, a 53km downhill mountain bike path from 1200m elevation to sea level.
With very steep sections, the triple brakes serve the purpose of redundancy.
bicycles.stackexchange.com/users/38078/Joseph Lust
Was just wondering if a dual option like this was possible or even desirable.
Can a bike have both rim and disc brakes?
bicycles.stackexchange.com
<brakes><disc-brake>
bicycles.stackexchange.com/questions/45611
bicycles.stackexchange.com/users/31791/user31791
It is possible to have rim and disc brakes, the usual configeration is disc at the front and rim at the rear. In fact, when disc brakes first appeared many companies produced bikes with this configuration and a lot of mountain bikes ran with a single disc brake (mechanical) at the front and a vee brake at the rear. However, both types of brake on one wheel is unnecessary as such a configuration would not have any advantage. It is possible to put different brake types on the front and back, which has some advantages when fitting panniers. Some frames have mountings for both types, and bikes can be sold using either. While it is theoretically possible to have one of each type on a single wheel, this may be difficult to implement while ensuring even force from both and the advantage is not clear on most bikes. Both brakes should be able to lock the wheel, so the added force would be redundant. Double brakes are used on some tandem bikes and tricycles, or for redundancy on some downhill bikes.
It is possible to put different brake types on the front and back, which has some advantages when fitting panniers. Some frames have mountings for both types, and bikes can be sold using either. While it is theoretically possible to have one of each type on a single wheel, this may be difficult to implement while ensuring even force from both and the advantage is not clear on most bikes. Both brakes should be able to lock the wheel, so the added force would be redundant. Double brakes are used on some tandem bikes and tricycles, or for redundancy on some downhill bikes.