If you have IP addresses of a set of computers (in a LAN), what other information can be deduced from them? For instance, is there a way to find out what operating system the computer behind each IP is running?
That depends if you mean passively or actively. Passively (that is, by not attempting to connect to or scan the IP itself) you can see exactly what information is available from an IP from my service at http://ipinfo.io. It includes rough geolocation, hostname, and network owner. Here the data for Google's public DNS IP:
$ curl ipinfo.io/8.8.8.8
{
"ip": "8.8.8.8",
"hostname": "google-public-dns-a.google.com",
"loc": "37.385999999999996,-122.0838",
"org": "AS15169 Google Inc.",
"city": "Mountain View",
"region": "California",
"country": "US",
"phone": 650
}
If you want to take the active approach you can find out much more. Tools like nmap will tell you exactly what services are running and be able to make a good guess at the OS that's running.