Xero is a hugely popular cloud accounting package.
Accounting is a good place for bespoke development to stop and packaged software to kick in.
The most common Xero integration is pushing invoices from the custom system into Xero. Also, retrieveing customer balances from Xero.
We have also synced Contacts and Items/products lists. This allows you to maintain single lists of customers and products without having to make changes in two places.