We love a free pattern as much as the next person! At the same time, you shouldn't let a few bucks keep you from a really great project! Let's take a closer look...
Free
Free patterns are great! Straight up: knitting and crocheting are hobbies that can get expensive. Knitting needles can be pricey depending on their quality, and crochet tends to take a lot more yarn per finished project. Often free patterns will come along with certain yarns or other purchases and you should absolutely take advantage!
There are also lots of great free patterns out there from larger yarn companies like Purl Soho or Cascade and designers like Tin Can Knits. Many are are designed for beginners and many to entice you to buy their yarn!
On the flip side, giving something away for free can (but does not necessarily) mean that there was less tech-editing or will be less pattern support if you run into issues.
Purchased
Buying a pattern means you are trusting that the designer has put the time in so you get a (hopefully, reasonably) frustration-free project. Designers are taking the time to come up with a project, do the math for you, test it, edit it, and photograph it. This is all worth paying for!
Purchased patterns are also more likely to go into detailed tutorials about unusual elements, offer more sizes, and generally be more complicated.
Companies will often put out seasonal collections of patterns to inspire you with new projects. Often you can get a price break if you buy a collection vs an individual pattern - which is totally worth it if you like more than one!
The Bottom Line
Typically, you get what you pay for. ;) Not all free patterns are rigorously tech edited and tested, and they tend to be simpler. Paying for a pattern isn't a guarantee that all will be smooth sailing, but the odds are in your favor! Plus, you are compensating a designer for their expertise.