A Google poll: I entered the search terms "congress letter email fax phone effective". All right, it's mostly boring, but if you're trying to avoid activist's remorse, it may be worth a look. Also, see if you can find the hidden snark cookie! Here's a summary from the top links; the short version seems to be that the more effort a contact costs you, the more likely the Congressperson's staff is to take it seriously:

Office visits: this is the gold standard of constituent influence. A well-prepared group meeting with the legislator or the staffer responsible for your issue is said to be the most effective contact.

Letters: a personally composed letter sent by regular mail is highly effective if you're in no hurry. Estimates of the delay run from 2 weeks to 3 months.

Fax: one source says this is the way to go since the imposition of the delay on letters. Other sources claim it's no better than email. My guess is it depends on the office staff.

Phone: a phone call is often said to be more effective than email. There seems to be a suspicion, whether well-founded or not I can't say, that email messages and internet petition signatures are too easily fabricated to be worth much. But not all phone calls are created equal. One site suggests a preliminary call to inquire for the name of the staffer in charge of your issue, and a follow-up call to that staffer. However, another source says it's unlikely you'll ever get this person on the phone! Amusingly, only one of my sources mentions the possibility of speaking personally with your Congressperson by telephone! Wonder why this group?

Email: some sources suggest a lot of distrust of email. Others say that if the message is as individual and thoughtful as a good letter, it can be quite effective.

Mass postcards: one step above petitions.

Petitions: least effective and may be ignored, most sources say.

More details:

On mass emails:

...many congressional staff question the authenticity of form communications -- 49% of staff surveyed either agreed or strongly agreed with the statement, "Most identical form communications campaigns are sent without the constituent's knowledge or approval."

Who reads it?

Representatives read a significant portion of their mail personally, while Senators typically ask their staff to select the most interesting and captivating letters. Congressional offices keep a weekly and, in some cases, daily count of contacts regarding particular issues.

On relative effectiveness

In order of MOST to LEAST effective, these are the means of contacting legislators:

1. personal visit to the legislator's Washington DC office or home-state office
2. personally handwritten but LEGIBLE short letter
3. personally typewritten or word-processed letter
4. phone call to a key staffer in the office
5. phone call to the reception staffers in the office
6. personally written fax
7. an obvious form letter or fax
8. personally written e-mail
9. an obvious form e-mail

In order of MOST to LEAST effective, these are the kinds of people who contact legislators

1. government officials
2. constituent organizations or corporations (entities in the legislator' home district/state)
3. individual constituents (voters in the legislator's home district/state)
4. major international, national or regional organizations or corporations
5. little-known international, national or regional orgs. & corps.
6. non-constituent individual Americans
7. foreign individuals, or foreign orgs. & corps.

On personalized letters:

Since congressional offices receive only a handful of letters on most issues, each carries real power.

From the same source, on composition and fax numbers:

Think about your letter as having three paragraphs, or parts. The opening part should clearly state your position and why you hold it. Urge the Member of Congress to take specific action (e.g. vote for/against a particular bill or amendment; co-sponsor a bill; etc.) The second part should give more information on the bill/action in question and evidence supporting your position. The third part should be a brief summary and provide final encouragement. When possible, try to thank your Member for some action they've taken in the past. To find fax numbers for your Members of Congress, log on to the Washington Office website at www.uua.org/uuawo and click “Advocacy Resources.”

and on phone calls:

Although not as effective as letters, telephone calls are very important—especially when the respective legislation is being debated or voted upon. A constituent will rarely get through to a member of Congress on the telephone, but talking to or leaving a message for the relevant staff person definitely has an impact. [...]

The U.S. House of Representatives Switchboard is (202) 225-3121; the Senate is (202) 224-3121. Be prepared to ask for your Member's office by name When you've reached the office, you can either (1) name the issue you're interested in and ask to speak to the staffperson who works on the issue; or (2) make your statement to the person who has answered the phone. The former is probably more effective; the latter more efficient. To find information about your representatives, see www.uua.org/uuawo.

and on emails:

Although few if any emails actually reach the Members themselves, most are seen or addressed by the staff in some way. How emails are handled varies widely from office to office—some will make sure you get a personal reply, some will send an automatic reply and nothing else.

Keep in mind that sending a letter through the mail is much more effective than an email. If you are going to email—which is certainly better than nothing—be sure to include your home mailing address in your message! Not only are you more likely to get a response, but your viewpoint will carry more weight.

Getting them to read it:

One member of Congress I worked for asked to see three to four of the most thoughtful and well-argued constituent letters per week, regardless of the topic or whether we agreed with the writer. Within two weeks of trying to comply with this request, I realized that we received, at most, one or two thoughtful letters a week. The vast majority of the correspondence consisted of form letters, postcards, and personal letters full of inappropriate language and personal slurs. As a result, the few thought- provoking letters received considerable attention from the member.

From the same: ask for a response:

A congressional office I worked in received a few hundred postcards as part of a coordinated campaign against privatization of social security. The printed return address on the postcards included the city and state only, making it impossible for us to respond. We simply threw the postcards away and devoted our resources to responding to people who had written personal letters about the issue.

From the same: on mass mailings and petitions:

In reality, one thoughtful well-argued letter can
have more impact than 100 postcards or petition signatures.