One correction. Connecticut has two Senators from the Democratic Party. Richard Blumenthal ran and won in 2010 after Chris Dodd retired. Joe Lieberman was a Democrat for many years. In fact, he was the 2000 Democratic Party Vice Presidential Candidate. Then in 2006, he was Primaried and lost to Ned Lamont. Lieberman ran as an Independent and won in the General Election. He chose not to run in 2012, and Democrat Chris Murphy won the seat.
For simplicity, I'll use the oversimplified Red/Blue discussion terms. The Northeast tends to be Blue, but some of the more rural Northeast states are arguably more Purple, which includes both Maine and Vermont.
On the gun issue of concealed carry, Maine and Vermont were two of ten Right To Carry states in the U.S. before 1987. 1987 was the year that Florida became a Right To Carry state, and that began what some term a New Wave of Right To Carry legislation. Maine and Vermont are two of the ten Old Wave states. Vermont in fact requires no license at all to carry a gun concealed.
Angus King, the current Independent Senator from Maine, is one of two former Independent Governors of Maine. He was a lifelong Democrat when he ran for Governor as an Independent. After 10 years out of public life, he ran for Senate and won as an Independent in 2012. He caucused with the Democrats, and after the Republicans won control of the Senate in 2014 he stated he would continue to caucus with the Democrats. He is pro choice on abortion, supports the Affordable Care Act (something no Republican Senator voted for), supports same sex marriage, opposes the Keystone XL Pipeline, supports background checks on gun sales, a ban on ammunition magazines holding over 10 rounds, but opposes an assault weapon ban.
Maine likes Independents. In 1992, Ross Perot got 30.44 percent of the Maine vote, the highest of any state in 1992. Bill Clinton won Maine with 38.77 percent. Perot had a much less spectacular year in 1996, but he got 14.19 percent of the Maine vote, the highest of any state in 1996. Bill Clinton again won Maine with 51.62 percent.
Bernie Sanders is the Independent Senator from Vermont. While some say that Angus King is a far left progressive, Bernie Sanders is a self described democratic socialist. He was a member of the anti-Vietnam War Liberty Union Party. After several unsuccessful elections in which he ran for U.S. Senate and Governor, he left the LU Party. In 1981, he ran for Mayor of Burlington, and defeated a six term Democratic Party incumbent. He won three more terms as Mayor, defeating both Democratic and Republican Party challengers, and the last time defeating a candidate endorsed by BOTH major parties. In 1990, he won Vermont's Congressional seat as an Independent becoming the first House Independent in 40 years. He's a cofounder of the Congressional Progressive Caucus, but voted against the Brady Bill. When Jim Jeffords retired from the Senate in 2006, Bernie Sanders ran for the seat and won beating Rich Tarrant by a 2 to 1 margin. Sanders won re-election in 2012 with 71% of the vote, and he is one of the most popular Senators in the Senate. He caucused with the Democrats, but can be very critical of some Democrats, including the President at times. He has indicated a possible Presidential run in 2016.
Maine and Vermont were in the Top 10 most Liberal states according to a 2013 Gallup poll.
Addendum on Dec 6, 2014
Independent is a very ambiguous term.
Some view Independent as not belonging to any organized political party, which in and of itself is a very vague and misunderstood act. Political party membership does not generally entail filling out an application, paying dues, signing anything, or even pledging support for the party. When one votes in a primary election--an entirely separate and lengthy discussion in and of itself--one is in some states declaring one to be a member of that political party, at least until the next primary. Under this definition, depending upon the state in question, the only way one could remain an Independent is to NEVER vote in a primary election thereby removing one from a portion of the voting process--arguably the most important portion.
In some states, in order to vote in a primary, one must declare oneself a member of a party so that one can then vote in that party primary. In my former home state of Maryland, one had to do this well in advance--several months if memory serves me--by completing a revision to one's voter registration. At the time, this had to be printed, signed, returned, and processed within the required cutoff. I remember years ago missing the cutoff deadline by several days.
In other states, one can declare the party for which one intends to vote there and then on primary election day in the voting booth. Choose a party, and then vote for the candidates in that party primary. In states that allow or require mail in ballots, one may receive a ballot for each of the parties with candidates running. Choose a party ballot, complete it, and mail it in. There may be candidates from parties other than the Democratic or Republican party running (e.g. Green, Libertarian) and one may be able to choose one of those parties when voting in the primary.
There may be non-partisan elected positions where a candidate does not declare their party affiliation, for that elected office. These positions may or may not appear in a primary election. They may appear in a primary election, everyone regardless of party affiliation can vote for a candidate in that position, and the top two or more vote getters then appear on the ballot in the general election. If they instead appear on the general election ballot, voters get to choose, regardless of voter party affiliation from the primary election.
One wonders whether there are states with a party that calls itself the Independent Party. If so, then the Independent Party candidates appear on the Independent Party ballot, which is now a separate definition from candidates who are non-partisan. Being an Independent may not be the same as being an Independent, or even an independent.
As one can see, the issue of being an Independent is very much entwined in the primary process in one's state. The only thing definitive one can say about an Independent is that they are a member of neither the Democratic nor the Republican Party, but so what? Are they mostly ideologically aligned with one of the two major parties? If so which one? The Green, Progressive, Reform and Libertarian Parties are certainly Third Parties, and perhaps Independents depending upon the definition, but they could not be more different from one another. There are issues where some agree, but still lots of areas where they disagree.
Some take refuge in the term Independent because it allows them to become lazy and not take a stand on important issues. Populism is another such term that is often used without an accompanying definition, and different people's definitions will vary widely.