My profession is fundraising so I have a little bit of experience here. Best advice is to make it easy to give and be sure to send a thank you promptly. Include self-addressed envelopes with a nice letter. The letter should detail, in specific, what you will use the money for. Last year, my collegiate chapter needed money for Homecoming to execute their Seasame Street theme--the list they sent detailed that Big Bird's feathers would cost them $20, among other things. Since I have a soft spot for Big Bird, I sent my check immediately.
I would stick to projects rather than just asking for general funds--some alum might not be comfortable giving if they think its will be used for the beer fund (of course, some may.) In the end, they just want to know that their money will be used responsibly or the way it was intended.
I'd also advise including a list of chapter donors in your alumni newsletter if you have one--this will recognize those that give, and possibly shame those who don't into sending their check pronto.
Possibly consider making a competition by class-- e.g. "The Alpha Class had 100% participation. Thank you!"
For my own giving, I give to my chapter and my org's Foundation annually. I volunteer for the Foundation. I have given to chapters I advise and I have supported projects at chapters other than my own, particularly new chapters. Generally, if I am asked, I give something.
Which reminds me, I need to pay my alumnae dues!
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