Steam – Are Dark Soul’s Steam servers VAC secured

There are two, and they are determined by a choice you have to make following the final boss fight.

Yes there are places that you can only get to by jumping. On the bright side however, they're not essential for progressing. Rather, they usually lead to some basic item or pick up. Off the top of my head, I've only discovered a light crossbow, bolts and one humanity in locations like this. Additionally, in most of these situations you can get past by rolling instead of jumping. From what I can remember, the bridge you're referring to is the most difficult jump I had to make.

The only other situation this is important, is done in order to return to the Undead Asylum (optional). You'll need to jump across to a ledge, but it can be done by simply rolling forward. Here is a video in case you're interested: