Hmm...
To start with, I think the story would have become darker early on.
Perhaps Sasuke would consider avenging Sakura, depending on how badly he actually cared for her when they were teammates. Anyway he would have another link to his village cut, so Orochimaru would have less trouble talking him into defecting.
Naruto would have the Pain Test (Can you forgive someone has taken a beloved person from you away?) early on. Without the lessons he received from Jiraiya maybe he would not be capable to forgive Gaara. However, If he was capable to forgive him, I doubt they would become great friends.
The Search of Tsunade arc would be mostly unaltered. After Tsunade healed Sasuke he would be still deadly jealousy from Naruto. It is likely he thinks Sakura's death reinforces his belief of friends are a liability. Naruto would not know what happened to Sasuke between Sasuke and Orochimaru (since Sakura was the only witness), so he would not understand why Sasuke was so hostile to him. Their relationship would become more fragile.
There would no be the POAL, but Naruto would want rescuing Sasuke all the same, because he would refuse losing another person.
During his battle, Sasuke surely would throw his failure to save Sakura on Naruto's face, declaring his method does not work.
Tsunade would no prized disciple to pass her lore on, of course. It is doubtful Ino became a medic nin. Maybe she would stop chasing Sasuke out of respect for her late best friend.
Kakashi would consider he had failed his teammates again. Still I think he would get back from it.
Part II would be completely different. Who would become Team Kakashi? Who would heal Kankuro? Who would take the puppeteer -Oh my God, I have forgotten his name!- down? Konoha and Suna would have a solid alliance? Naruto would be emotionally invested in saving Gaara?
And what of the search for Sasuke in Grass Country? Naruto might have died right then should Sakura not having healed him. Or he could have lost control over Kyuubi. And maybe he would not be so invested in rescuing Sasuke.
It is funny thinking about how different would be the history without Sakura in spite of her haters claiming she does nothing.
Fandom-wise, and given what I have seen happening when a love interest dies, I suspect out of nowhere Sakura would gain a ton of loud supporters and would become the most venerated character of the fandom. Thousands of fans will storm Naruto boards to openly cry over poor Gwen Sta- Sakura Haruno, whom the main character loved and was tragically murdered, and fantasize over "what-if" scenarios. NH fans would find them most annoying.
I do not think Naruto would have another love interest, anyway.