Pair annihilation processes usually result in the production of two photons. However, since quarks are mediated by the strong interaction, they more often result in two gluons (governed by the strong interaction).
But, due to quark "confinement" (which essentially means that quarks cannot be observed outside the particles they compose) we can't observe this through the normal scattering experiments we use to observe such phenomena. However, quarks annihilating into two photons can be observed in processes such as neutral pion decay. The πo is composed of either a down and anti-down quark or a up and anti-up quark. It has been observed that the πo decays into two photons, which means the quark and anti-quark that composed it annihilated!
Also, while not defined as pair annihilation, a quark and antiquark of different types can also interact in a similar way when they interact due to the weak force (which means they are mediated by W- and Z-bosons). These processes can have a variety of outcomes -- two gauge bosons, another quark and anti quark, etc. Note that the pair annihilation process also can result in two gauge bosons, but the type of bosons that can be produced depend on the original particles. For example, a quark and its respective antiquark can annihilate and produce two Z-bosons. But, an up quark and an anti-down quark can annihilate and produce a W+-boson and a Z-boson. The fact that W-bosons have charge is what makes these processes possible. Since W-bosons have charge, they can change quark flavor, as well. So, an up and anti-down quark can interact and produce a down and anti-up quark, if they are mediated by a W--boson.
These types of processes are precisely what were studied at the Tevatron at Fermilab. The Tevatron collided a proton and an anti-proton beam and analyzed the byproducts of the quark-antiquark interactions (the quarks from the protons, antiquarks from the anti-protons) in order to better understand these types of processes (but mostly to see if anything weird happened!)
Feel free to follow up if you have any more questions!
-- Natasha S.
(published on 05/07/11)