Overturning the ban on hunting and allowing CDs and DVDs to be copied are among the most popular petitions listed on the Downing Street website.
Hundreds of signatories have called for the repeal of the Hunting Act
Number 10 launched the scheme to allow people to petition Prime Minister Tony Blair online, saying it encourages more campaigners than "ever before".
Iraq, ID cards, inheritance tax and making Spandau Ballet's song Gold the national anthem are among the topics.
Party political, obscene and libellous petitions will not be included.
The most popular "e-petition" so far is one calling for the repeal of the 2004 Hunting Act.
It made hunting foxes with dogs illegal in England and Wales, but hounds can be used to follow a scent and to flush out a fox.
Among the signatories is someone called Ken Livingstone - although it is not thought to be the person of that name who is currently mayor of London and a vocal opponent of hunting.
MOST POPULAR SO FAR
Repeal Hunting Act
Change copyright law
Do not replace Trident
Levy tax on inefficient lightbulbs
Scrap ID cards
The next most popular "e-petition" on the site calls for an exception to copyright law, which would allow people to make copies of their CDs and DVDs.
There are several environmental ideas, from rationing petrol and diesel to taxing inefficient light bulbs.
The issues range from the international - there are calls for inquiries into the Iraq war - to the local, such as reviewing the roadworks on the M1 between junctions 8 and 10.
One petition is simply to "get people to stop bullying other people".
All e-petitions not put on the site would be listed in a separate section, with reasons given for their rejection, a Downing Street spokeswoman said.
The website is funded by the taxpayer, meaning party political material should not be included.
The spokeswoman said there was a "fine line" in deciding which e-petitions to reject.
She added that all paper petitions delivered to Downing Street in person would still be accepted.
No "inflammatory" statements or swear words are allowed on the site, while calls for actions "outside the remit" of the government are forbidden.
The system also prevents users from submitting the same petition twice.
Tom Steinberg, director of mySociety - which built the site - said: "We are trying to make it as transparent as possible.
"We will try to list all the rejected petitions and, even if we can't use the exact wording, if the petition is libellous, we will explain why it wasn't included."
No 10 says there are anti-spam measures and people who want to sign a petition have to give an e-mail address and a UK address including postcode, or an overseas address.
Last year, TV chef Jamie Oliver delivered a 271,677-signature petition to Mr Blair calling for improvements to school dinners.
The government later announced it was putting £280m into raising nutritional standards.
On Remembrance Sunday this year, families of service personnel killed in Iraq delivered a letter signed by about 750 relatives and veterans to Downing Street, calling for the immediate return of British troops.