It's absolutely possible for a 737 to land without thrust reverse, and I'd be quite confident that any narrow body jet, and perhaps even some heavies can as well, it just depends on the situation.
There's lots of variables, but if you land for example with 11,000 feet of runway, a slight headwind, no one landing behind you, and land in the touchdown zone, the ground spoilers alone with get you slowed to 80 knots with plenty of room left, and that's just one of many many examples. It's our SOP to always go into thrust reverse, but in reality, we'd just barely go into it to have it armed, and mostly coast to a stop.
Thrust Reverse saves brake wear and in a hot climate, limit the brake temps. which is important for aircraft turnaround time, but it's also true the planes are certified to stop without T/R.