Yes. News about cruise mishaps has cropped up in the past few years, but believe it or not it’s extremely rare for big problems to occur on cruises. They’re quite safe, they’ve been operating for decades, and they seldom have big problems. That said, it’s always better to opt for the more reputable cruise lines when possible, and travel insurance is a good idea no matter where, when, and how you’re traveling.
One factor to take into consideration is which destinations your cruise will be stopping in: if there are issues or travel warnings about those countries, it may be better to choose another cruise route. Cruise services, though, are actually quite good about modifying their routes to avoid any danger, so it’s not a huge issue.