I think it really depends on a lot of things, particularly, your metabolismm, how overweight you are . . . and if you're actively looking for changes or not! Personally, I lose weight quickly when I actually get my butt into motion. I've lost weight since I started exercising and eating less crap in the last two weeks, it's noticeable to others (at least one other person who I asked lol). Before I noticed that I had less fat on me, I noticed that I had more muscle, particularly in my calves (and if you're walking and running, you'll probably see increased muscle mass there first too), then my thighs.

Even if you don't lose weight quickly, remember that a slow weight loss can be better - it means it's less likely that you'll gain it all back. Sustainability is far more important than how quickly it happens!

Good luck

edit: I forgot to mention, the closer you are to your ideal weight, the slower the weight comes off. Of course you should weigh whatever you're comfortable with, and BMI charts aren't accurate for everyone (most Drs will tell you that, I believe), but if you become underweight, it's just as unhealthy as being overweight AND it's very difficult to maintain, can damage your metabolism, etc.