In short, yes! Absolutely, runners should strength train.
Many have taken this blog post by me to mean I don't think strength training is valuable. Even when I originally wrote that, somewhere around 15 years ago, I believed strength training is critical. I still question whether lifting weights is the best way to do that for most runners, though.
For most runners who have limited time and energy for training, I think we should be looking for ways to get the biggest benefit from the least amount of time. Going to the weight room is not the answer for this. Instead, I strongly believe that body weight exercises are the way to go.
I created a video on YouTube some time ago with a base routine that hits all the major muscle groups used in running. In my opinion, this is a good starting point for most runners. It covers a lot of ground including general work for most problem areas runners have. I do have other videos with more specific exercises to target specific problems but those are only available to Club HillRunner.com members.