Strength training for running is my forte, LOL.
Core strength is important as a runner - see the list of exercises I recommended for Allie, planks in particular, push-ups as well (since those are really more full-body), and I would also say things like plyometrics. Jump lunges, jump squats, box jumps, ski jumps. Just be careful with those and don't over do it and hurt yourself. I see people doing plyo moves incorrectly and IMO it's easy to hurt yourself when you're doing them wrong and going quickly. Go slow first until your body really knows the move, where it's very much muscle memory, then you can add speed and intensity later.
I will pretty much never not recommend squats. So squats. Body weight is fine, or you can do them holding something heavy if you want more, which I always do. God gave me big fat thighs so I might as well squat heavy. You can do them with dumbbells if you don't have a barbell, I've also been known to throw a dog across my back or put a dog on each shoulders and squat my dogs. =P A pistol squat is a great variation if you're doing body weight, very effective for a runner.
Lunges! Bulgarian lunges I tend to find very helpful for running, as well as just a regular lunge and side lunge.
Deadlifts, you can do these with heavy things around the house or dumbbells. Single-leg deadlifts are a thing as well, kind of like the Bulgarian lunge, it is quite helpful for runners.
I like rows a lot, it works your arms and your shoulders and also your lower back. Somewhere there is that shoulder video I did... here it is:
http://www.youtube.com/watch?v=tSrEYjA0PBw
I do rows in here and an overhead press, both of those are great for runners. The clean & press is a fave of mine but I also love burpees, so take that as you will hahaha.
For anybody who wants to do a race, I always recommend signing up for one and then telling everybody you know about it. Once you sign up, you have a real deadline, a date of when This Will Happen. And once you tell everybody you know, they'll help you hold to it. That's what I did... I knew if I told people and they knew what I was planning to do, my pride wouldn't let me back out LOL. And I knew they would all hold me to it too. Sign up, put it on your calendar, and then tell people!
