They will give you recipes and, very occasionally, small gifts via mail.
Being a game where you do the things that you want to do though, if making friends isn't what you want to do, don't do it.
However, arguably the most important thing that making friends does is it gives…
The game's story
Being a farming RPG, arguably just making friends is part of the benefit. There is a story (more story than “plot” since it's not linear) to Stardew Valley, and it's revealed by getting to know the NPCs.
Not making friends is like running around in Skyrim without ever doing the main quest: totally doable and it can be lots of fun and entirely fulfilling for a given player, but from an objective measure it results in missing a significant percentage of the game's content. (No backhanded criticism is implied here! This is how I personally play Elder Scrolls games.)
But again, this is a matter of taste. Getting to know the NPCs can be fulfilling in the same way that playing To The Moon is. But for those who like the Tycoon-game aspects of Stardew Valley more than the To The Moon aspects, the game is clever in allowing the player to find and focus on the things they personally find interesting. As one review put it:
The flexibility and freedom in Stardew Valley is without a doubt its greatest strength. It is one of those games that gives you so much autonomy that it ends up becoming more of a roleplaying game than anything else. Your avatar in the game adopts a personality through your actions. Are they helpful and neighbourly? Are they looking for love? Or are they driven to explore the many mysteries of the village? Worryingly, my character seemed to have become a paranoid recluse, scuttling into town only briefly to buy seeds before returning to his ramshackle farmhouse, his dog and his ever expanding patch of parsnips.