People could also be prompted to give money when they fill in tax returns or apply for passports, driving licences and other state services, the Cabinet Office suggested.
The initiatives were among measures set out in a consultation paper which ministers hope will make charitable giving - of money and time - a "social norm".
While Britons are generous with their money compared with those in almost all other countries, they rank only 29th for volunteering - spending 17 times more hours watching TV, it noted. But ministers said there was evidence of a "latent demand to give" that could be tapped into using new technologies such as mobile phones and social networking.
Individuals and businesses needed to be reminded of the "warm glow" that resulted from helping others, they concluded, with concerns about red tape and waste addressed to make giving easier.
Encouragement could include "thank you letters" from ministers to donors and a weekly television plug for National Lottery winners who give some of their windfall to good causes.
Public services will also be encouraged to take on more volunteers, in a move the government denied was an effort to provide public services "on the cheap" amid swingeing spending cuts.
The Cabinet Office minister Francis Maude said the government should not try to "compel" people to give, but unveiled two taxpayer-funded schemes aimed at encouraging involvement.
Local donors' contributions to projects in the most deprived areas will be matched through a 50 million Community First Fund and 10m match-funding will be available to voluntary projects. Under-used government buildings may also be opened up for charities to use.
The consultation document called on UK banks to look at copying a system used in Colombia that allows customers to make a donation each time they withdraw cash.
It paved the way for a national "round up the pound" scheme which would allow people to donate "change" when paying by debit or credit card.
A working group of businesses is to be set up in the new year to discuss how to expand it.
Mr Maude said the consultation - which runs until 9 March and will lead to firm proposals in the spring - was a key element of the Tories' "big society" agenda.
"Giving is too often caricatured as worthy and selfless, a one way street, but there's nothing wrong with doing things for each other and repaying kindnesses," he said.
"If we can agree as a society the values that underpin helping each other we can unlock huge potential for a stronger, bigger society."