Farmers are not rich and powerful. A subsidy is a result of the market prices for ag., which is a perfectly competitive market (no extra profit). However, now that prices are rising, a subsidy is not needed (see my first post).
As far as tax breaks go, you have to realize that there are multiplying effects within a capitalistic market place. If a multi-national is able to lower its corp. income tax, it can increase production and investment, which increases in the demand in a labor market, so it effects everyone down the chain and encourages business cooperation.
When it comes to lobbying, EVERYONE has a lobbyist: nonprofits like Red Cross, Easter Seals, etc. But yes, big business like Microsoft and Exxon-Mobile do too.
Lobbying is simply the active expression of a citizen's right to influence government. This right is fundamental to democracy, and it is guaranteed by the First Amendment. "The Congress shall make no law... abridged... the right of the people to peacably assemble, and to petition for redress of grievances." Moreover, lobbying is not an American invention. It is a way for citizens to advocate to the government, which is the foundation of any democratic body. To restrict this, the US government would regress without citizens' ability to express and proliferate thier political ideals.