Trick 1: Start a fight
Everybody knows the good old "Go-to-lounge-for-a-drink-and-wait-who-joins" trick.
But did you notice that, not unlike in real life, lounge chit-chat can be a little boring at times?
We humans, sadly, strive on conflict. So why not start a fight with somebody?
Of course, you should mail that player first and ask if he would also like to do some character development with you. But every player should be able to discern between IC and OOC relation, so while your IC characters could hate each other, OOC you can still be friends with the player and playing an enemy who gradually becomes a friend can be much more rewarding than the ever-friendly. Like Picard in that great episode "Enemy mine"!
And as a side note, you can involve engineering if you damage something in your fight or medical or security of course :-). And instantly, you play a storyline with at least 3 others.
Then, the longer you play that character, the more IIC memories he has with the other charachters, and the more you have of those, the more your character starts to 'live' in your mind. He becomes more and more real, developing his own personality by what he experiences in interaction with the others. And sometimes even you will be surprised by the character he develops :-)
-Julia

Trick #2: Hidden background
One of the things I try to do with every character is not just give them a background, but give them one or two important stories that aren't on their bio that you can introduce to the crew. It doesn't have to be crazy, but is should make sense for your character and help them evolve. These story arcs often take months to play out, so you always have something interesting to inspire your writing. And you can involve others on the ship too. The key though is to be flexible and allow for your interactions to take your story in directions you never imagined.
I do this also. As a matter of fact, my character on this ship is ~primarily~ about a story that isn't fully revealed on his bio, and will probably involve most of the crew before it gets fully revealed. His bio is a bit sparser than I usually write them, but if you pay attention you might notice something doesn't make sense about it.
But I'm not going to say any more about that. ;)
-Linds

Trick #3: Hobbies
Give your character a hobby. Everyone has something they enjoy doing outside of their work and if you place yourself in the right circumstances you can end up with some really funny/interesting/though provoking threads.
I'd say there are two types of hobbies you should consider giving your character: ones that establishes something about who they are, and ones that could make for interesting side-sims. You can have one that does both, but sometimes they act at cross purposes. The best hobbies for side-simming purposes are ones that involve other people, or can involve other people easily. Painting itself isn't so great, but painting other people could go somewhere.
- Linds

Trick # 4: starting a relationship
You have a look with whom on the roster you didn't have any dealings with yet. Then you read this character's bio, and if it's good you can find some inspiration there for a relationship that would work with your character. Love, hate, friendship, tutoring big brother/sister-like,....
You can mail that player and agree on a mutual background, like e.g. You two were at the Academy together and loved the same girl, or.... In order to give the relationship some depth
Contrary character traits are equally as much fun if not more, than similarities ;)
- Julia

Trick #5: Limitations
Your characters should have limitations and you should be aware of them when writing. I don't just mean obvious limitations like physical ones, but things like what they don't know and what kind of stresses they can't quite handle. "What they don't know" are probably the most fun to play with, since it can lead into all kinds of awkward situations that can be the basis for a relationship between characters. Once, a character of mine and someone else started an adversarial relationship that lasted for months simply because his character confused baseball with another sport, and my character didn't know what steampunk was.
- Joe

Trick #7: Ship's specs
Just like people can give you inspiration, so can places. Just think of your last holiday.
Say you read in the ship specs, that there's a hot tub. And right away you can think about a funny situation with another crew member in there.
The same goes for a gym, an arboretum, something specific for your ship.... also something specific for your department. Have a loc at the specs what your department's facilities have to offer.
That can give you IC inspiration for an everyday chore that might turn out different than the days before while on duty.
- Julia
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please, you are welcome to add your tricks.... :-)