It depends on where the beams are facing. If the magnetic poles are facing you and the spinning axis is facing the right position, then both can. So it depends on two things:
Direction of magnetic poles
Direction of spinning axis
The magnetic and rotational axes don't have to be exactly at 90 degrees to each other to see both beams. They only need be approximately at 90 degrees (depending on the 'opening angle' of the emission cone).
So there are plenty of pulsars that satisfy this and have two peaks in their profiles (when we observe their emission) that are approximately half a ...
Several pulsars have double-peaked profiles: you get two peaks per rotation, with one peak stronger than the other. An example of this is the Crab Pulsar. This suggests that at least some pulsars have two beams. Remember that the gravitational bending of light in the vicinity of the neutron star makes it possible to see a larger fraction of the surface, ...
Yes. One of the features that helps this scenario is the gravitational bending of light close to the neutron star, which allows for a larger fraction of the surface to be visible at a given time.
Many pulsars have double-peaked light curves, for example here's the light curve of the Crab Pulsar. In the pencil beam model these peaks correspond to the beams ...
NICER observations of PSR J0030+0451 in x-rays show hot spots clustered near one pole. The hot spots are presumed to be the termination of the active magnetic field lines, so there is really no magnetic "axis". The field is more complicated.
First surface map of a pulsar
The other answers cover the geometric part, but that only tells you what fraction of pulsars are seen as such from Earth. The other issue is what fraction of neutron stars are pulsars at all. If they don't pulse, and they don't do something else conspicuous like accrete from a binary companion, neutron stars are very difficult to find. A common rough ...
It is believed that old pulsars may have their rotational axes closely aligned with their magnetic field. This would happen over a timescale of $\tau\sim10^7$ years (Lyne & Manchester (1988)). There are three sets of phenomena driving the dynamics of the alignment (Casini & Montemayor (1998)):
Short-term ($\sim50$ days) variations caused by glitches
This is really about the nature of physical theories - we have observational evidence and a (falsifiable) theory has been posited to explain what is happening. The evidence since that theory was posited has served to reinforce its claims to correctness.
(But all magnets we have observed are dipoles - in theory monopoles exist but have never been observed. ...
The probability of seeing pulsed emission from a neutron star is simply the fraction of the sky covered by the beam, i.e. the beam solid angle divided by $4\pi$ steradians.
The angle swept out on the sky by a pulsar with an emission cone of width $\rho$ turns out to be
covering a fraction of the sky
Out of 100 pulsars, how many will have a beam that crosses the Earth?
"The beaming fraction f , that is the mean value of the fraction of observable pulsars or the mean probability of observing a normal pulsar, is 0.124 ± 0.004." M. Kolonko et al.: On the pulse-width statistics in radio pulsars