Typically no but you could. Depends how fixed, protected or exposed your installation is. IF the wiring is sealed up in conduit, nah. If it's a loose extension cord sort of arrangement, having an in-line fuse would probably be a good idea.
as for sizing it, figure out what either the safe carrying capacity of the wiring that came attached to the panel. But if you are wiring it yourself, then size the wire and fuze to something that can comfortably handle the peak power of the panel that's energizing the circuit. 150W panel at 12v is ~13A. Depending on the capacities and efficiencies and needs of your system you could fuse it down to 10A (on the theory that most panels rarely do better than 80% of their (peak) rating anyway, so you won't be cutting anything off, but might be blowing fuses at peak output, OR you go 15A on the fuse and wire capacity and lose some fractional power to the increased resistance of the thicker wire.
Beyond a basic safety level, it's all tradeoffs and compromises, depending on your own preferences or comfort levels.
And the whole thing is predicated on how drawn down your batteries get overnight and how much power your charge controller allows to pass, anyway. Your system may never even come close to sucking in enough juice to need maximal fusing and wire gauge on your panel. But that also presumes there's never a failure mode or cut / damaged / shorted wire and maximum amp flow. In which case you are again back to fusing to protect ignition of the wire (or anything else downstream of your power source, the panel).
Think of a fuse as a throttle limiter. Your wire has a max safe capacity. The fuse keeps the current flow BELOW that. And at the same time you don't want that set so low that you can't get the most out of your panel.
And panel space being at a premium on a vehicle-mounted or -borne system, you want to make that max flow possible to eke out all you can get from the panels, for the times you really need it. Ideally your panels system's total rated output is say double your anticipated power consumption. That gives you buffer for ACTUAL panel performance vs its factory rating, gives you buffer for poor panel positioning / capture angles, loss of efficiency in transmission, conversion, partial shade on the panels, loss of performance over lifespan of the panel, etc etc.
And then all the compromises start. Size, space, placement, COST, etc etc.