A strong core is not all about the six or eight pack, so even if you struggle to do 50 abdominal curls it doesn't mean you ignore this area of your body. We use our core muscles all the time. From carrying shopping bags, gardening and picking your kids's up, with all of these movements you are constantly engaging your core muscles. When people think of the core muscles the main area seen is the stomach/mid section. Actually you posterior chain is also included in this section. Many niggles such as shoulder tension or lower back pain is due to a weakness in this area. By strengthening these core muscles you will naturally develop a better posture. This will in turn encourage all the muscles to work how they should without any over compensating and hopefully reduce these niggles we often feel on a daily basis.
You can use gym equipment to target the core muscles, such as a cradle or an actual abdominal curl machine where you can add resistance to work against. But even if you are a regular exerciser working this area can be challenged by simple body weight exercises. The core is also an area you can work every day unlike other strength workouts where you need 24-48 hours rest in between sessions. The beauty of not using equipment is these core exercises can be done anywhere at any time. All you need is the self discipline to put the core to work!
A strong core will not develop straight away. You will need to learn how to engage these muscles. Attending a pilates or yoga class will help you understand what muscles need to be worked in what way.