Yes! Nepal is absolutely safe to travel in.
Some potential trekkers having certain qualms about safety and security while on a holiday in Nepal may have read about some trekker being robbed or faced a life-threatening situation. Very rare cases like this have happened in recent times but in such rare incidents , the victims have been those traveling alone or in just a pair without a fixed itinerary in areas which all trekking agencies specifically warn about. In the fifty-plus years since tourism opened up in Nepal, such incidents can be counted on the fingers of one hand.
Like in any country with fragile political systems, there can always be turmoil and disorder at any given point in time, such as the ten-year long insurgency of recent times. But even then, there were no instances of tourists/trekkers being harmed or threatened or robbed.
Despite hyped-up and baseless reports in the international media and panicky embassies handing out negative travel advisories, in the last half-decade, hundreds of thousands of tourists/trekkers/mountain climbers have come to Nepal and enjoyed their holidays in complete safety and returned home. Wherever they go, be it village, town or city, they are welcomed with warmth and hospitality by the Nepali people. Police security arrangements are always in place and assistance, if needed, is always promptly given.
There can be other areas of safety concern such as accidents or sickness while on trek in the high mountains and hills but these are incidental and quickly addressed.
Yes, Nepal is safe to travel in.