Hi Eli - core to my mind core work is essential. I don't mean every day for an hour - but maybe twice a week for half an hour just to keep things working.
For me it became a real problem. 2 years ago I was out running and swallowed a fly! I coughed involuntarily (as you would) and popped a disc in my spine. Agony!! Anyway over about 3 weeks it got better and I started running again but always had lower back pain. Not bad enough to stop me but over the next 2 years it got gradually worse. I saw physios, chiropractors, sports therapists, podiatrists - no one could get to the bottom of it. My disc was fine and no problem with my spine. This year I went to the physio for what i said would be the last time. Though whether i ran or not my back hurt. It wasn't running causing it. What he discovered was i had no core strength at all. When I hurt my back all the supporting muscles "turned off" to the injured area. This is what happens when you injure any area and as you heal they "turn on" again. because i'd started running too soon mine never turned on so other muscles took up the job that my core should do. So I was constantly plagued by tight glutes, ITB, hamstrings etc. I was biomechanically a mess and needed to completely re-train my core.
None of us is biomechanically perfect. We all run a tightrope that when everything is OK we can run without a problem even though we might not be as strong in some areas as we should be or bits of us are tighter than they should be. However, if we become injured that can kick off a chain reaction that takes time and a great deal of effort to correct. That is why your core is so important - it's the mainstay of successful running and running injury free.
If you are running OK a pilates class once a week, or a fitball class plus half an hour at home should keep you strong. We don't need a core like Jessica Ennis (though that would be nice!) to keep running but a little maintenance goes a long way to protecting yourself. Just be aware though that "core" doesn't mean "abs". Its not a six pack you're after but the supporting muscles deep inside that you're after.... though a sixpack does look good as well!
Now I'm much better I do a pilates class or fitball once a week and one half hour at home. I generally do about 30 reps of about 6 different excersises.