There are many Halachos that a leftie does with his left hand and those that he does with his right hand. For example Shema is always done with the right hand even if you are a leftie. By which other Halachos does a leftie use his right hand too?
R' Paysach Krohn wrote an English-language book on halachos for lefties. It's available free by mail if you call his home; he lives in Queens, New York, and is listed. (Obviously, you might want to pay him for it, and the postage.) The book is arranged in sections, one of which is a list of things lefties do the same as righties, and another of which is things lefties do the opposite from the way righties do; so one whole section of that book answers your question. (I'd copy things therefrom, but can't locate my copy.)
Edit: I've now discovered this book online. (Thanks to Dr. Melech Tanen for linking to it.) He has twenty-one subsections devoted to things lefties do with the right side, of which the following are about the right hand specifically (as sought in the question):
- Cover your eyes with your right hand for sh'ma.
- Give tz'daka using your right hand.
- Bless a child on Friday night by putting your right hand on his head.
- Tap your chest with your right hand during confession.
- Put on your right sleeve before your left when dressing.
- Pick up the cup with your right hand for washing hands on arising.
- Pour water over your right hand first, when washing hands on arising or for bread.
- When holding onto a sefer Tora with one hand for an aliya, use the right hand.
- When doing birchas kohanim, your right hand should be slightly above your left.
- Look at your right-hand fingernails during havdala.
As always, for practical halacha, consult your rabbi.
This chart is pretty interesting.