Well, it kinda depends what side you are talking about.
The battery side needs some kind of overcurrent protection, either a breaker, or a fuse. The rule is that the fuse/breaker is there to protect the cable. So generally I tell people to put a fuse/breaker on the output side of the MPPT, sized for the cable.
Regulations require the PV side to have fuses too, and you need to fuse both sides (positive and negative). Jaco is right that in a single string, the PV modules will deliver a maximum of around 10A or so (for the typical 72-cell panels we install nowadays), so you will put a 12A fuse inline. Do remember though that fuses derate when they get hot, so in my own system I had to resort to 16A fuses because they kept blowing every few months. Again, it has to be sized for the cable.
Now on this topic (the PV side): the PV modules can never deliver more than their short circuit current, so under normal conditions, a fuse should never blow, since even a short circuit on the PV side will not exceed the size of the fuse, the normal operating condition of the panel is pretty close to the shofrt-circuit current anyway. But… you also want to protect against abnormal conditions. Imagine the MPPT is damaged and it allows battery current to flow backwards through a dead short somewhere on that cabling… you want the cable to be protected.
Furthermore, if you have multiple parallel strings on a single MPPT, a fault in one string could channel current from the other parallel strings into the faulty one. This usually only becomes a problem once you have 3 strings, but again, for multiple parallel strings you definitely want to fuse the strings individually before combining them.
Long story short: The fuse/breaker is there to protect the cable. Always put one in, unless you can mathematically prove that the cable is already sufficiently protected by existing overcurrent protection.