Which types of hydrogen bonds are known to exist in RNA secondary structures?
By far the most common type of base pair is the Watson-Crick base pair in an RNA helix. Those are comparably easy to predict, e.g. Mfold and the Vienna RNA package can do this.

Base triples, three nucleobases that form hydrogen bonds to each other are not uncommon in RNAs with a complex tertiary structure. There is even a database of RNA triples, though this one also contains triples where not all three bases make contact with each other.

There are also quadruplexes, but there each base only makes contact with two other bases. I don't know if there are any structures where one base makes contact with more than two other ones.