Define what you mean by "worst". Least safe? Least amount of things to do?
As far as the most unsafe neighborhoods in Seattle, downtown Seattle would take the cake - and by extension, many of the neighborhoods bordering it such as Belltown (although I think otherwise Belltown is a very cool neighborhood) and Lower Queen Anne. The International District and SoDo border downtown to the south, and are also very unsafe.
Continuing south, you have most of the least safe neighborhoods in Seattle: Rainier, the general vicinity of MLK, most of Beacon Hill, South Park, Othello, Skyway. The only real exceptions to this are Bryn Mawr and Seward Park.
If you go into West Seattle, the standout is White Center and surrounding areas. Most neighborhoods north and south of White Center are pretty safe, and I personally think West Seattle is a pretty cool place.
Now, if we go north it gets a little more complicated. The obvious areas to avoid are Aurora Ave N and the Lake City neighborhood. However, there are some very popular areas of north Seattle that are statistically not very safe such as Capitol Hill and Fremont, which are both really cool neighborhoods! I have spent a lot of time on Capitol Hill personally, and I've never felt unsafe there. However, it is a pretty grungy neighborhood with a very active nightlife scene, so it can get fairly rowdy there especially during Block Party or on weekends. This area also attracts a lot of Seattle's homeless population (as does downtown), particularly Broadway / Pike and Cal Anderson after dark. Although I have spent many nights in both of these places and haven't ever felt threatened like I most certainly have in south Seattle. I haven't spent a lot of time in Fremont, however I hear it also has a fairly active nightlife so that could be the issue there, as well.
Now, if you're talking about neighborhoods that are just boring and isolating, then I would have to say you are pretty hard-pressed to find that in Seattle. In my experience living here, I would say that Beacon Hill is particularly bad (super residential, absolutely no restaurants or interesting shops at all, hardly any grocery stores!) - I know my friends and I were miserable when we lived there because there was nothing to do in our neighborhood. I would also say that there are some more residential parts of very north Seattle (especially towards Shoreline) that are mostly like car dealerships, box stores and fast food restaurants - however, most neighborhoods in north Seattle have a lot of great local shops and restaurants. Of course, the Industrial District / SoDo is going to be pretty boring, although Georgetown is very close by and has a lot of good restaurants and artsy shops. There are also certain parts of West Seattle that are pretty undeveloped - again, car dealerships, box stores and fast food - mostly the area between Admiral and White Center.
Hope that helps!
