An opportunity to proselytize, I see.

Personal skills:
Well, when the brown-stuff hits the fan, crowd control and mob psychology certainly come to mind. Kung Fu fighting skills, where you can dodge spears being thrown at you a la Cain in the opening credits of "Kung Fu," are useful. Knowing the tenets of Swimming with Sharks is a must (http://www.uwm.edu/People/bmaas/misc/howtoswim.html).

Technical skills:
Oracle. But what does that entail? Knowing the ins and outs of every single feature? No. Definitely includes the features you are using, and staying abreast of what is coming down the road (new features, getting off deprecated features before you have no choice, pertinent bug fixes, and so on).

Keep/make a little black book of things you need to know like right NOW in case there is a major problem. It's like an emergency procedures checklist. A minute or two skimming the steps on how to restore a ______ (fill in the blank) may save you from pulling an all-nighter trying to un-goatscrew the mistake you made.

Knowledge of the underlying OS - if you are on UNIX, what would it take for you to know what it takes to be a junior UNIX SA? Same with Windows. Self-sufficiency cannot be overvalued.

Read a lot of books/documentation. If you have access to MetaLink, use the bookmark feature to store useful articles.

Programming skills can only help you, especially PL/SQL. Knowledge of Java helps too (using the jar command, for example).

Know installation inside and out. Comes in handy when trying to install other Oracle products (9i Application Server & Developer Suite, for example, lots of conflicting documentation on disk and memory requirements, sometimes no information on what you need for environment variables).

That's a start. I'm sure others will be happy to add their perspective.