By chance – Por acaso

I found your site by chance.
Eu achei o seu site por acaso.

Over at WR, they explain that ‘por acaso‘ has a few other meanings, such as ‘in fact’ and ‘as a matter of fact’. Learn more here.

By the way – A propósito

- You are leaving, right?
- Yeah, I am.
- Oh ok. Are you going to the city, by the way?

- Você está saindo, não está?
- Sim, estou.
- Ah tá. A propósito, você está indo à cidade?

Use ‘a propósito‘ when you wish to say “in addition, but of less importance”.