Social desires:
I want to be respected. @Ganymede phrased this as 'I hope to entertain' and that resonates but I'll go a step further and admit that I have a certain need to be admired and appreciated. I rarely do things with intention to harm other people, but this is partly because if others feel bad because of me, I feel bad about myself; I want my contributions to add positive value.
I want healthy separation. Despite the above, what I want from the community is to feel wanted, not needed. If I start to feel like people are making demands of me or that my contributions are no longer seen as voluntary but an expectation I have to meet, I peace. I want the freedom to come and go as I please, RP with others outside of my usual circle, and choose what I participate in without being judged for what I choose not to. I never want to have to explain why I do or don't want to do something.
I want a "professional" relationship, with fellow members of the community being more akin to colleagues than friends. This is a controversial one, I'm aware. This relates especially to displays of affection and familiarity and especially one-to-one. My interest in engaging with someone communally or for RP purposes doesn't necessarily mean I want to engage with them individually for OOC purposes, and expressions of admiration on my part are not an offer of lower social/sexual/romantic boundaries between us. I take care not to invite the assumption that it should, and will avoid people who show signs of misinterpretation/desperation.
Personal desires:
I want to pursue omniscience in a world full of mystery. To find out what makes every character tick, what the relationships are between them and the overarching story. For this reason I tend to play spies, scientists, hackers and detective types — people who have an excuse to go digging or interrogate people one-to-one. When I get into romantic storylines, it's likely to be with a character I find complex and interesting to try and figure out, who throws me a lot of curveballs and maybe even starts out as a rival, so there's initial resistance to tease out curiosity. I avoid characters who come across as very flat or don't give me a lot to work with, and I avoid settings that feel too predictable.
I want social commentary. (I think this is also a controversial one.) The setting has to provide some room for ideological conflict that goes beyond just light vs. dark, good vs. evil, nice vs. bully. My characters aren't often a reflection of my RL values, in fact they'll often be the opposite specifically because I want to act as a foil, make people think and give people something to criticise.
I want shock, horror, awe, action, adventure, impossible choices and exceptional circumstances. Take me outside the confines of RL humdrum, I'm here for a thrill-ride. If I engage in bar RP it's to set up the connections/investment for when things go awry or to decompress/commiserate/celebrate whatever cool big thing we just survived. But I want what really drives and holds our IC relationships together to be those major events, not day-to-day or smalltalk.
I want tension tolerance. It's fine if our characters don't get along. It's fine if things don't always go our way. It's fine if our lovebirds won't get their happily ever after. It's fine (good actually) if the stakes feel high. It's fine if I can't cleanly put your character into a box of friend or enemy. I like it when things aren't straightforward and am comfortable with uncertainty, changing dynamics and unexpected roadblocks. Don't make things too easy for my character; it'll bore me and the story I'm pursuing is more often about the challenge they face than the finish line.
These are not all needs, some of these are just wants. And if other people communicate their needs, I will often be happy to accommodate as long as I'm likewise having fun. I'll adjust my playstyle to the setting, community, and my current RP partner and can slow-roll things until I understand their comfort levels. (I will default to the assumption that you don't want an epic rivalry, for instance, and keep things ICly cordial and fluffy until I get the go-ahead to assume otherwise.)