I also came from a BlackBerry and notifications are one of the weak spots on an iPhone (especially unjailbroken). You basically have two choices, sound or vibrate. When you turn on vibrate, everything vibrates.
Like Bad Ash said, you can use different ringtones for different contacts, as well as (6) preselected text notification sounds, but there aren't different sound choices for any other type of sounds including email notification.
There aren't any repeat reminders either, except for texts which you get another notification maybe 30 secs after the first. You get one notification and that's it, one of the things I really disliked when I first got my iPhone.
If you decide to jailbreak, there are more options for notifications. I use IntelliScreen and ToneFXs. These aren't free apps, but they allow you to change any of your sounds to what ever you would like, as well as adding repeat notifications. They are definitely worth the money for me. IntelliScreen also adds the BlackBerry "Today" screen to your iPhone's lockscreen so you can see emails, calendar appointments, etc.
And if you didn't know, there is also a way to make any drm free song in your iTunes library a ringtone.