A resonant half-wave dipole is typically fed with coaxial feedline and tuned to a specific area of a band. Its planned use is generally within that band, although it may be useful on other bands (near odd-harmonics) where feedpoint impedance reasonably matches the coaxial feedline. The well-known length formula is L (feet) = 468/Frequency (MHz). This formula is an approximation. Antenna height, leg angles, insulation, wire diameter, and surroundings affect a dipole's resonant frequency and impedance. It is better to initially make the antenna a few percent longer than calculated and trim it back to size (higher in frequency), although dangling pigtails will work to slightly lengthen an antenna (reduce frequency) without adverse electrical or mechanical affects.
A popular misconception is because the dipole is resonant, or because the dipole feedline is small in diameter, a balun is not helpful. There are also questionable claims that "feedline radiation is good", or pattern change without a balun is insignificant. Many of these claims contradict each other. If one is true, the other claim argues against it. That is what happens when we justify a questionable practice.
Indeed there are cases where a balun is not needed at the balanced to unbalanced transition between coax and dipole, but they are very specific cases where the feedline is suspended in air from the center of the antenna straight away from the feedpoint, and is grounded ¼ wavelength away from the feedpoint.
Omitting the balun in other cases will often cause feedline length to affect SWR, increased noise in the receiver, increased RFI, or any combination of these ill effects. In unlucky cases with higher Amateur power levels permitted, omission of a balun can cause coaxial shield or connector arcing to tower legs or other metallic objects.
The best balun for this application is a 1:1 ratio current balun.