Until fairly recently I used Michelin latex tubes with non-removable cores, still got them on my old 700C bike. In recent years, the quality of these sems to have declined, or maybe the stock in my LBS is just too old (latex ends up by perishing), so I now have Schwalbe butyl tubes on most of the family bikes.
I spent a fair bit of time looking for my first leak with Schwalbe tubes, the pressure wasn't sufficient to reveal it when immersing the tube in water. I replaced the tube.
The second time I had a leak I tried unscrewing the valve and found out that the core is removable. I don't have a special tool, so just tightened it with a 6" adjustable end wrench.