So, I'm going to choose "growing up" to mean "late teenage years" because while mobiles technically existed before then I didn't know or care what they were.
First phone was a Phillips Savvy. I got it because it was cheap but SMS were 20c each and I didn't really have a job, so I mostly just called people or messaged people and asked them to call me.
Then I got a second-hand Nokia 5110 which was more expensive but really common. You could buy new plastic fronts/back and swap between them. Great phone but it died when I accidentally broke the screen.
Ok, so the first phone that I loved (even though I didn't like the design) was an Ericsson A3618 because, even though it was still monophonic, it had a ringtone composer built into it. So I'd sit there making my own weird ringtones.. and it had Tetris. So I guess that's the answer.
The last phone I remember having before getting a Blackberry at work (and by definition far from "growing up") was a Siemens C55. Polyphonic ringtones, prince of persia... it was pretty cool.