Selected answers from the Dumb SEO Questions G+ community.
Simon Cartier: Yes, hosting is linked to rankings or at least it was before December. Shared hostings share an IP and so if some sites you share the hosting with are spammy etc. it will affect you, hence why getting dedicated is recommended for first page positions
Alan Bleiweiss: Simon Cartier is referring to the "bad neighborhoods" concept where one site can be implied to be potentially untrustworthy due to the "company" it keeps. Except from an IP and hosting perspective, it`s EXTREMELY difficult to assign a high enough level of validation that one site is unworthy of ranking JUST because of the shared hosting environment they`re on. It`s near impossible, in fact.
Google looks at many other signals and does not just rely on a single potential factor like this. You can use a tool such as GetSignal`s Reverse IP tool that lists other sites on the same block, if you want. Personally, I don`t bother with it. However you`re free to do so, and if you think you can tell whether enough other sites there are toxic enough, you can look to have your site moved. Is it worth the effort though?
Trey Collier: Changing your hosting provider can have an effect on your rankings. One example of why would be changing from a very slow provider to a very fast provider could have a positive effect on your rankings overall. Vice versa if you go from a fast to a slow provider.
Wissam Dandan: the location of the server might affect it ... i do remember a test that was done on builtvisible ? where they were hosted in uk and then moved to US servers
Jeremy L. Knauff: Where web hosting will have a real/significant effect is page speed. Beyond that, you should be running on https anyway, which requires a dedicated IP, so any worries about other websites are unfounded.