There's two situations with KSing that you have to worry about.
Taking a kill from a rager.
Some people don't understand the value of single kills. Sure they could be on a snowballing champion, but if they get an assist and free farm for a bit they should be able to get another kill from their xp advantage. If this is your situation it might be best to ignore them, depending on how detrimental they will be to your team if you do.
Taking many kills as a non-carry.
Most champions scale well with kills, and so getting kills will always be an advantage. That said you do not want a 9/0 tank or support while your carries only have assists. Having your kills focused on someone not designed to deal damage is actually a good way to throw an otherwise easy win. There are ways of getting around this of course, like having a carry who scales well on xp, or can make due with farm and assists, but all of this must be taken into consideration. Just keep in mind there is a reason there are two carries in a typical meta styled match, so make sure one does not get underfed in an attempt to feed the other.