You can have both notifications and a persistent history with the majority of IRC clients. Many public channels keep logs, even. If someone pings me (hilight), then I get an urgency hint. Most window managers handle urgency hints. I use openbox + xterm + irssi. I do get notified if someone pings me, and I can also add any arbitrary words for which I would get notified. With a small Perl script I could use notify-send if I wanted (it probably already exists).

If you are really referring to phone notifications, well, you can use an IRC client on your phone, then you would get notifications on your phone. I use irssi even on my Android phone.

Let us not forget that there is the other side of the story: many people report that they have been enjoying life more without those phone notifications.

I love IRC. I have been using IRC ever since I was 11. It made me a more technical person. I find that IRC is not that easily accessible to the majority, which is a good thing, because of this, the conversations tend to be of higher quality, and technical in most channels. I would also like to add that IRC is the reason I understand English, and a zillion other things. :)