I've done the whole self-initiation thing. Several times, in fact. First there were rituals based on Wiccan texts, then more personal creations, based on some pantheon or philosophy that I felt was the bee's knees at the time. And of course they all felt in some way significant at the time.
I guess it largely stems from the simple coolness factor of being part of some specific tradition, society or whatever. But I'm kinda past that phase in my occult career (I hope). I don't really feel a need for a faction, just having an alignment is plenty. (A bit of geek humour there.) I try to see the world as a whole, rather than through the eyes of a specific tradition. And there is no initiation into the whole Universe except for birth.
Now, initiation into a group is a slightly different matter, I surmise. It can obviously make you feel more strongly a part of it. But I don't belong to any group, and am generally somewhat sceptical about such things, seeing as how I see spirituality as a particularly personal thing.
And I fail to see how such a ritual could have any kind of impact on one's magickal abilities, even though there are many writers who rave on about the importance of initiation in one's magickal development. Of course a ritual affirmation of your faith and intentions can be helpful, particularly for the beginner. But I don't see it as in any way compulsory. In the end, magick is about you and your relationship with the Universe, while initiation is about your relationship with a particular group. There is a difference.
Others see initiation everywhere, and various events and aspects of life as part of some great metaphorical initiation process. I just call it 'life' and leave it at that.