I'm going to bring it up to my boyfriend that he hasn't bought me a birthday gift
You really want a gift that badly?
I don't like that he forgets me, and I want him to know I like having nice things.
Won't reminding him kind of kill the desire to want the gift, though? Plus, not to be rude, but I think you should lower your expectations.
Well, I know my boyfriend isn't rich, so I'm alright with just a simple gift.
It's a little rude to expect a gift, but at the same time, if the gesture of a gift is really important to you, you should communicate that to your boyfriend. He may not know.