Alistar is one of my main champs, but I notice that I almost never kill anyone with him. Just one or two by luck, so I normally build myself as tank.
Is there any build or anything that can help me? Or is it impossible? Even if I can't be a super killing machine I would like to make more damage.
Don't worry too much about trying to get kills - Alistar's role in a match is to provide support and disruption. You may not get many killing blows, but if you're a decent player, you should have many many assists instead.
If you're worried about losing out on the money that comes with kills, I'd suggest you look into Gold/10 items on Alistar - Philosopher's Stone and Heart of Gold being the better of the 4 for him. (Duplicate items don't stack, but there's nothing stopping you from picking up one of each).
That said, Alistar makes good use of Sheen, which is a cheap way to double your basic attack damage, and gives him mana to boot.
If you're playing as a support/tank, then kills are not your goal. In addition to gold generating items, I'd also suggest the masteries that boost gold or exp on an assist.
Before the V1.0.0.116 patch, it wasn't uncommon to see AP builds on Alistar. His ratios have been reduced pretty significantly, but it's still viable to build AP on him to increase his damage. Try it in an AI game first though. =D
I think the important thing is to tell us how you play your ali... dual lane with ad carry? then you're supporting and not worrying about getting kills... you at least get the assist money and can help your team with wards, aura items and such... if you consider play some Shushei'ish AP alistar you probably want to take a lane you can farm it up, or at least have a partner who isn't that dependend on CS... I think you can play alistar in many ways but he's not that depended on kills that it would greatly impact your game... you can get your build faster but he isn't like fed vayne who once with full build isn't stoppable anymore... your key moment with ali will be the engaging teamfights and wether you get the kills or not, if you engage correctly you will most certainly win your teamfight and that's what matters in the end I think.. :)
Even if I can't be a super killing machine I would like to make more damage
This is fairly important as a tank, if you're not dealing damage, then you'll only be CCing and supporting with your heal, which is nice, however a tank that does next to no damage can often be more or less ignored. Adding a bit of damage - you are a much bigger threat, so they wont ignore you once your CC is done and burst down your carry then turn on you.
As a support class you really shouldn't be trying to get kills, as a tank I wouldn't say go for the kill, or ever KS your carries, but you can add damage which means sometimes you will get the kill, you'll need to be fairly in their face anyway as a melee class so don't worry about it.
