[snook32]

I make a grapefruit "cider". I'm calling it a cider because I ferment it with cider yeast and age it along the guidelines of a cider. The entire process is no different than apple cider, except no apples are used.
What category would this fall under or can it be entered into competitions?  It seems the cider categories refer to apples as a base. Any information would be appreciated.

[lupulinmax]

Cider is an apple based beverage.  Maybe a fruit wine or country wine category in a wine competition would be a better match.  Sounds like an interesting drink using grapefruit.

[hopfenundmalz]

There is the Perry categories, made from pears, so not just apples.

No idea where a pineapple wine would go. Will defer to someone more expert.

[dmtaylor]

I believe the fermented juice of anything other than pears or apples is called wine.  Hence there are no BJCP guidelines... but you might be able to find wine guidelines elsewhere.

[tomsawyer]

I've made grapefruit wine before.  Stuff is pretty tasty if you like grapefruit.  I make mine dry but it would probably be good to backsweeten to an off-dry.

You could probably put a little malt extract in it and enter it as a fruit beer, or add some honey and enter it as a melomel.  Backsweetening with honey sounds good too.

[Jimmy K]

I don't think there is a category for it. The process of making wine and cider are similar - the main difference is the base - cider is made from apples, wine is made from other fruit. Early on in the BJCP, amateur wine competitions already existed, but they ignored mead and cider. So BJCP added mead and cider categories for those neglected styles. Basically, all the misfits got together and formed a band.
 
That said, if there character is "cidery" you could try entering it as specialty cider. It will probably be up to the judges how much they want to see apple character. Don't be surprised if you loose points for not being apple based though.
 
Or you could make one with some apple and enter that as fruit cider - but the apple character would need to be prominent.