I may be wrong but I feel like it's easy to default into thinking that having a strong core means you have tight and defined abs. At least that was my logic for a while. And it makes sense, right? If you have defined abs clearly your core is strong. I can't tell you how many sit ups I did when I first started working out that try and obtain this. A word to the wise, this will NOT get you cut, chiseled or a wicked six pack. Save you some Russian twists, you're welcome ;)
A strong core will develop as you workout more. Naturally, the core is being used when doing run, bike and swim workouts, and it will begin to get stronger the more you train. But this is the way I see it. Your main workouts--runs, bike, and swim sets--are like your meals, you need them to sustain yourself. So then 'core' workouts and lifting are like your vitamins, you need them to supplement what you don't get from your meals and they help fuel you so together, with the meals, you grow stronger. As a triathlete though, most of us are already stretched for time between two workouts a day, how does one fit in core/lifting workouts? Well much like any other supplement, it needs to be taken within proportion. Meaning, you should be doing core/lift workouts as you feel necessary, but at least once-twice a week for 20 minutes. Before I hopped into tri training I found pleasure in doing long and heavy lift sets with a workout partner, so I look forward to my lift sessions, 2-3 times a week. And as far as core goes, I'll do it before a bike workout in the middle of the week or after a long run....although some times those runs wear me out and I end up pushing it off.
Ok, so to wrap it up, the last thing to address is, "What are some good core exercises to do if not sit ups?" Right. Well for me I like doing sets and switching it up so I attack all the parts of the body. This week's core set went something like:
3X (5 pull ups, 15 burpees, 15 box jumps, 15 regular squats, 10 one leg squats--5 each leg--, 20 forward lunges--10 each leg--, 15 push ups, 15 tricept dips) Rest 2-3 minutes in between sequence but not between sets!
**If you need to add resistance because this is all too easy for your badass self--use some weights but don't forget, doing this three times through will make you tired
I think it's important to mix it up though, do things that are uncomfortable to you and once you get used to it, change it up. The best way to change your body is to keep it guessing. I have found that writing out my workout, or having on in my head helps. And there are a lot of great resources out there for core exercises. Not to mention Youtube has some great videos that demonstrate almost any and all core moves.
2-3X (20 side-to-side twists with weighted ball, 20 crunches on yoga ball, 20 side crunches (each side) on ball, 20 crunches w/ yoga ball in between feet & bringing up above you while simultaneously reaching hands up to touch the ball (I use a 10lb weight in my hands now to add resistance).
So go out there and get your core on! :)