A Google Web Search Help thread has a complaint from a worried searcher who stumbled upon a Google Suggestion on how to kill yourself. He said he was searching for tips on killing poisonous mushrooms and when he began typing "how to kill," Google suggested he search for "How to killing yourself."
Here is a picture:
Google does sometimes censor the suggestions in the list but typically they are algorithmically driven based on searcher popularity. In this case, it might make sense for Google to filter out these suggestions.
The topic of suicide ads showing up in in AdWords is nothing new. Also, in the past we talked about Google censoring both the ads and organic results for suicide matches. Although censoring results is typically something Google is against, censoring the suggestions is something they have historically done and should do here.
Forum discussion at Google Web Search Help.