I would like to improve on the first post in this suggestion, was actually going to make my own but did a check first to see if there was already any made.
The current way XenForo handles alerts is suited for a small number of alerts, people can practically "alert spam" you by liking 20/25 of your posts (or even more). It is forcing users to turn off alerts for certain things which is counter-productive to keeping them engaged. I really urge XenForo to improve their core notifications feature.
Merge notifications of similar nature:
As with Facebook currently, its much better if notifications of similar natures are "merged", especially likes on same post, profile post comments etc. Currently if 100 members like a single of your posts you get 100 alerts, and you are forced to turn of alerts for likes. Why force a user to do this when it could be merged into one alert which states "ABC, XYZ, WPQ and 97 other members liked ...." <- this keeps the user sane and avoids the user turning off alerts for likes.
Most admin/moderators will understand my situation because their posts are the ones that get the most likes, especially announcement posts or event posts and such, and you are forced to turn of alerts for likes because that clogs most of your alerts and makes you miss important features.
Merge notifications from same member (likes):
I agree that @ user tags and Quotes don't need to be merged, since they are content unique and such and there is a way to limit their notifications from going to members, but when a single member goes and likes a number of your posts, let's say A member likes 120 posts by B member (let's just say that user posts content thats really helpful and likeable) technically A member isn't "alert spamming", he/she is just showing appreciation. But B member gets annoyed due to the new 120 like notifications, XenForo can also fix this by merging those alerts as in: "ABC liked your post in the thread {link here} and {link: 129 other posts}"
The "link" for other posts just opens up a new page or maybe merge it somehow with "likes received" to show likes given by that certain member.
I think this will only make everything better and users won't be forced to turn off alerts which really is bad because the alert/notification system on XenForo is good and keeps users engaged, if they begin to turn off alerts just because of getting too many you know something is wrong.