To replace Access, you can use OpenOffice.org Base. I would suggest doing a test run, first with the most complex databases. Base doesn't have much in the way of calculations within the database, though it does have some reasonable query and reporting features. You can find ways of bringing data into Base here.
Regarding a bookkeeping application, I haven't used any. However, options include TurboCash, Lazy Eight (also written as Lazy 8), Emma, GnuCash, jGnash and QHacc.
This was first published in November 2006