What do you like best?
There is free tier usage, you can select from decent amount of DB for your proyect, the most known and useful, such as SQL Server, Oracle, MySql, MariaDB etc. Also they are very customizable, you can create instances on your own needs, you can select the resources for you applications or services, like hard disk, memory ram, iops, even the region where it is allocated to get better ping, very easy to use, easy to connect with another databases, is perfect for scalable projects.
What do you dislike?
If you don't be careful of free tier usage, you'll get some surprises billing on your credit card. If you are novice with RDS, maybe can be a bit hard to understand all the features it offers, but there are many guides which can help you.
Recommendations to others considering the product
Use free level use, for proof, before use the paid version, but keep in mind that the free level may have some restrictions which the paid version don't. You will not regret if you pay for this service, there is everything you need and more.
What business problems are you solving with the product? What benefits have you realized?
I am web, software, and app developer, right now i am current user of aws, for many projects, i use others instance like ec2, neptune, s3, etc. RDS have helped me a lot, when i need use external relational data base, to make apis, or anyother scalable project as gameservers. it make so easy the way to send and get data.