I have trained with free weights for over 10 years now. Both my upper body and my lower body strength have increased dramatically. I do not experience any lack of flexibility or movement because of weight training, but I do get stiffness if I do not regularly stretch (regardless of whether or not I weight-train).
There is one negative though. Although my grip and arm strength certainly assists my Aikido -- I find I rely on strength to ‘muscle' through a technique sometimes instead of improving my form (because the strength is there and it's naturally easier).
That's a training issue though -- something that can certainly be overcome.