Should a speaker attend a conference where he/she is required to pay their own registration fee? I have been accepted to present a paper at a conference in a recognised university. 

There is no doubt about the 'legitimacy' or public standing of this university as it is recognised worldwide. In addition, it is the management department within the university that is organising the conference. The keynote speakers are recognised and leaders in their fields.

The conference has two streams: peer review and non-peer review. The non-peer review is more like practical / application of theories in practice.

I am located in the non-peer review section and was asked to pay my own registration of $500. There is no assistance for travel etc.

Is this normal for an international conference? (I always thought at least the speaker's registration was stand expense that was borne by the conference organisers).

What are the pros and cons of attending and presenting at such conferences?
Most international conferences are paid for by the registration fees of the attendees.  The higher the ratio of attendees to speakers, the more registrations the conference can afford to comp (give for free).  When a large fraction of the attendees are also speakers, as is the case with a lot of peer-review-centric conferences, then it's often the case that only the keynote speakers have compensated registration and/or travel.  If the conference is close on its budget, even the organizers are expected to pay their own way and their own registration fees.  The smaller the conference, the more likely this is to be the case, but even very big ones often expect everybody but the keynote speakers to pay their own way.

In short: yes, this isn't unusual at all.