I too was 'naturally' disorganised when I was younger - forgetting/losing things, being late, missing deadlines, etc.
I have now become MUCH more organised, to the point where people who know me now simply can't believe that my family still regard me as 'the scatty one'. So it is totally possible, and much easier than you think to change.
I would say the most important thing is to work out WHY you are disorganised - here are a few possible reasons (although by no means exhaustive, and I'm not saying any of these are necessarily you):
A way to manage people's expectations of you - if you are known to be a bit all over the shop, people are less likely to ask things from you. Similarly, if you're always pulling things out of the bag at the last moment, it means that you have an 'excuse' if something's a bit under par - "well, I think that's a pretty good report, considering I hadn't had any sleep and finished it at six in the morning" etc.
A way to opt out of less agreeable tasks - if your time management is always right down to the wire, then you feel you are 'allowed' to disregard the things you don't want to do.
A way of passively showing that you aren't happy/coping with your life - the classic cry for help (BTW a 'cry for help' should always be heeded, not disregarded, in my opinion :) )
A feeling that you work best under pressure - this one is slightly trickier, since many people genuinely do their best work under a tight deadline. If this is you, then you need to factor this in, rather than trying to work against it.
A way to 'test' how much the people around you notice/care - it can be very reassuring when people drop everything to help you out of a hole of your own making. For example, a friend of mine (who would never dream of being late for work, etc) regularly shows up hours late to social functions or doesn't show up at all. In her case, it's a mixture of social anxiety, and wanting to get the reassurance of everyone saying 'so you made it at last! Hurrah!' or 'we missed you last night. What a shame you couldn't make it.'
Ordinary common-or-garden laziness - being organised is more boring and less exciting than everything always being in a flap. If you consider that the effort of organisation isn't actually worth avoiding the hassle of being disorganised, then you'll lack motivation to change.
Phew, sorry, that one is a bit of a mammoth post - I'll stop now :)