How can I find out what other websites are hosted from my website IP address and why is that important from SEO point of view?

To complete the other answers, there is no authoritative database of complete IP -> name mappings.

DNS provides for two kinds of mappings:

• name -> IP. Multiple names can map to a single IP
• IP -> name (aka "reverse"). A given IP can map only to a single name.

Whether there is actually a reverse (IP -> name) mapping and what it points to is subject to the policies of the "owner" of the IP address (the web hosting company in this case). But it will not provide an exhaustive list of all names that map to that IP.

The services referred to in the previous answers try to assemble such a database, by making a not of all name -> IP mappings they find which point to said IP. But the number of domain names is huge and constantly changing, so they can hardly have a complete list, just whatever they found.

The only ones who may have the whole list (and that is actually not necessarily the case) is your web host, however I doubt they would share this information.

Of course, this would only be an issue in the case of shared hosting where many different sites are hosted on the same server with the same IP address. If you have a dedicated server (or equivalent) with you own IP address, then this would not be an issue.

However, note that all sorts of classification methods (e.g. for spam) will consider whole blocks rather than individual IP addresses, so even in that case, if you're in "a bad neighbourhood", you may get penalised by the behaviour of your neighbours.

Don't know if it's possible with simple command, but there are special "Reverse-IP" services just for that, check that one for example: http://viewdns.info/reverseip/

Apparently if you share IP with other domain, that is considered... malicious, like it's sending spam or spreading some viruses or having some "illegal" content, then your good domain also will be affected or even completely blocked by search engines. However if all domains on this IP are good, it should not have much effect (theoretically).

To answer your question directly: No, in most cases there is no negative impact for sharing an IP with a bad domain. How do I know this? I am the SEO oracle. I come from the future to save humanity.

Kidding, but only sort-of. If there was such a thing as IP penalization, we would be seeing far far different search results than what we do today because many domains wouldn't have gained authority. Here is what I mean:

• Shared Hosting Plans. It's not uncommon for poor quality hosts such as hostgator, 1&1, or others to pack over 400 tenants onto a single server. Allowing one of those to wreck the momentum of 399 others would be devastating. Riots would ensue, flaming torches, pitchforks, and hordes of angry OP's would be at Google's doorstep overnight. Google is not that stupid.
• Rented Ecommerce & SaaS. Let's take Bigcommerce for example. They use multi-tenant IP's so you will find many stores along side yours when looking up rdns. Looking at the domains you may notice that they are extremely low quality, repetitious, etc. In many cases they are straight up spam. Now let's go a bit further. BC allows you to run a demo store, which uses some of the same routing assets as the live stores. Your demo utilizes things such as util subdomain routes. Demos are often abused, used for spam, etc. Those routes should be toasted from SERP's, but they aren't. Again, Google is not that stupid.
• High Churn Cloud Servers. The biggest brands in the world use Google/AWS/Digitalocean alongside the biggest slimeball botnets in the world. They are always in close proximity to each other. Maybe Netflix can afford AWS enterprise which guarantees a cleaner IP, but 99% of the rest of folks using the service can't. More slimeballs churning throwaway instances to get away from banned/wrecked IP's via AWS means more IP's with shady historicals. The ratio of bad IP's to good IP's may someday get significant, which can make AWS look bad. Google is not that stupid to make AWS look bad. It's in their best interest to keep on indexing that service in a fair manner.
• IPv6 Saturation. There are just too many IP's to keep track of. 340,282,366,920,938,000,000,000,000,000,000,000,000 of them to be precise. IPv6 means each person alive on earth can have 5x1028 IP's allocated to them...enough to make them "disposable". Thats too many to track and far too many to worry about until you make a big big ripple. So in light of these numbers, is 1 IP hosting 1 crap spam domain out of 400 on a server big enough to cause a ripple for the rest? I don't think so. Is 1 botnet C&C running its own VPS with a couple of phishing sites beside it enough to cause a ripple? You bet. Worrying about Mr Spam's IP in an infinite sea of disposable malevolency is not sustainable. Worrying about heavy hitters doing the same thing on their own instances IS sustainable. Google isn't that stupid to spend all resources on small fries, at the IP level. They use the domain and other levels instead, which makes sense.

As you can see, IP isn't as important as people think for SEO authority. All the rank factors start to hit at domain level, and they are semi-conservative + transparent (as in, it's obvious if you are doing something wrong). Here is a link exploring that thought: https://moz.com/search-ranking-factors/correlations#6

So when does IP authority actually matter? Server side email delivery and client IP bans. That's about it. Does that matter for SEO? Nope.

PS: there are a few tools to rdns, you should try them all. I don't know of one that runs easily since it requires an "index" of the net to find neighbors. Since they are "crawlers" the website tool results may vary. One rdns site may show a domain on the IP that the other missed. Another thing you can try is SSH into your shared server if they let you do those sorts of things. Check out the user list and start hitting the server IP followed by username like so to see what kind of neighbors you have: 123.123.123.123/~username

PSS: We tried Bigcommerce once. Our IP was pre-junked, mail server abused into the ground by demo store spammers, mail server was in RBL's, and neighbors were crap halfbaked stores, but our brand new domain gained PR3 and first page rankings in less than 2 months, without any backlinks whatsoever. If that IP mattered, we would have stayed buried.