Weight Training and Running

I am trying to combine a weight training program with my running program, but would like to know whether it is a good idea to run when the muscles are quite sore after weight training. Am I doing more harm than good, as I do not want to put myself at risk of injury?

I have been doing a combination of weights and running for 3 years now.
Do you mean running straight after using wieghts?
In the past I used to do a run to warm up then use weights, nowadays I only use wieghts Monday and Wednesday then do my runs on the days in between.
everyone is different but it is better to be safe than sorry.

Sorry I should have clarified what I meant. I did a weight training session on Sunday with heavier weights than usual, and now my thighs feel as if they have had a severe pummeling which I am told is the muscles building themselves after they have been broken down. I want to go running, but don't know whether this is a good idea or not. Any advice?

I go weight training 3x per week & go running 4x and have no problems, running the following day should be no problem (might feel as though you've got lead legs at first ) but the benefits of combining the 2 will be noticeable in your running after a few sessions of leg work. To me it seems like i'm not putting as much physical effort into my running as my muscles have become more efficient! The risk of injury through weights is only the same as now i.e warm up first to reduce risk.
P.S. I also use the rower in the gym its a really good for cross training works all the body.