1 - Solo piracy. With PvP increasingly feeling like an ultra complex extention of the spreadsheets-numbers game, I'd love a chance to just get down to me, my ship, and a target - and then that targets oh-so-delicious tears as I personally take him apart (or even more welcome, honest recognition of a good catch).
2 - I have an interest in 0.0 as well, and I'd honestly like to fly under one alliance/bloc banner for the duration of a campaign - i.e., from the initial scouting/intel-gathering/target selection moments until long after the last killmail, when all the dust has settled and the aftermath has been layed out.
3 - Successfully lead/be a director in a corp. My first attempt was... a learning experience (read: an utter disaster) and my second was somewhat better, but hindered by the fact that I have an overwhelming desire to go out and shoot stuff when I should be organizing. In other words, I want to lead a corp, and have other people do all the work for me.
4 - An entirely IC (no random nullsec blob, no unaffiliated mercs, just RPers) epic hotdrop/titan bridge into the middle of an RP event that completely wins the day. Possibly the holy grail of RP possibilities for me, due to A, a severe lack of RP possibilities and B, lack of IC hotdroppable stuff and titan bridges. But yes, that beautiful "Uh-oh, cyno, get read- OHHOLYSHITAMARRFLEETOUTOFNOWHERE!" moment? That's what I want to do before I leave EVE.