You can use this to your advantage by using Pulverize and following with Headbutt to push them into your turret's firing range. Be aware that skilled players will know this gimmick and will not fall for it unless they are caught unaware.
Using Pulverize immediately after a successful Headbutt will apply the stun from Pulverize. Instead of being pushed back, the target will be knocked up and stay in place. This can be useful in some chase situations (make sure you succeed or you will knock them further away), or finishing off a weakened opponent on the run. This tactic is risky, leaves you useless while both abilities are on cooldown, but is considered a staple move of Alistar and used very often in both competitive and casual play.
In the event that a tank is running close to your target to protect them, a safer and often more useful strategy is to use Headbutt on the tank to get you into range to Pulverize your true target.
Be wary when using Headbutt because you might end up disrupting positions in a way that benefits the enemy team, particularly knocking them out of a teammate's area of effect.
Alistar is considered a great roamer due to the fact that all he needs is his Pulverize and Headbutt combo to gank a lane.
Hitting an enemy into a close-by thick wall with Headbutt will stun them for ~1s. Reason being that they will still try to travel the distance even if a wall is in the way. Thus they will be stuck against the wall for the duration of the flight.
However, if Headbutt is used near a wall, it sometimes sends the enemy onto the other side which allows them to escape.
This can also be used to your advantage. Sending the enemy tank or a high damage dealing carry (like Fiddlesticks after he uses Crowstorm) over a wall can allow your team to win a 5v4 match.
Most walls in the jungle and river are thin, but whether they will go over them or not depends on how close they were to the wall at impact. If they are a high priority target, it may be better to keep them in the fight. A high priority threat would be neutralized if knocked over.
Flash can be used on Alistar to quickly get into the middle of a team, hit much of them with Pulverize, and knock a squishy target toward his team with Headbutt. Always spread out when you see Alistar walk toward your team.
Beware the potential combo of canceling the knockback of Headbutt into Pulverize. At that note, it is safest to poke Alistar with something that is farther than the 600 ability range of Headbutt.
Due to said significant cooldowns, crowd-controlling his own team as he uses Pulverize if possible can waste the ability's synergy with his allies and leave Alistar with little else to do for his team while it cools down - as long as you yourself have other things to use while you traded cooldown(s) of your own for his, of course.