There is a wide variety of presentation tools with all kinds of features. However, for an academic presentation (I assume that this is what the question implies, otherwise it is off-topic on this site), animated transitions between slides and, for the most part, on a slide are highly recommended against. The main reason is that they significantly distract an audience from the essence of the presentation, thus, negatively impacting both the audience and the presenter.
When referring to the on-slide transitions above, I said "for the most part", because there are cases, when on-slide animated transitions are actually appropriate and helpful. For example, when a particular slide describes dynamic elements or nature of a system, it is helpful to illustrate the dynamics of changing state of the system's elements or features with animated or otherwise dynamic transitions.
Speaking about presentation tools, most software offerings (standalone and online services) offer the rather basic features that you mention in your requirements. For example, besides Microsoft Office and Libre Office, you can take a look at academically-focused
Beamer (very flexible and highly recommended) and
knitr software, as well as online services Bunkr, Speaker Deck, already mentioned RevealJS, Prezi (don't like it and don't recommend - similarly to @Nox, I get dizzy from their standard transitions), Keynote (AFAIK, it's Mac-only), SlideRocket and many more. If your subject matter allows story telling (which is what should be the core of ANY presentation, regardless of the domain), but in a more visual way, check Amazon StoryTeller and PowToon.