While I understand the cynical sentiment (and mostly agree with it) -- I can assure you an email to your congressperson will get a response. Wife used to be a staffer several years ago for her district's rep and would look for trends in emails and then pass those off to the rep and his writer to handle responses.
Sure, an email might not seem like much, but enough of them will at least require some sort of consideration.
"You can write an email to yourself."
AKA
They are going to read your personal email anyways...
Have there been any studies done that show any correlation between number of calls/letters a politician's office receives, and how they actually vote on bills proposed?
I've contacted my state and national representatives dozens of times over the years and have found that methods of contact seems to get noticed by the staffers (who are in most cases the only ones who will ever know that you contacted the office) in the following order:
Email - generally ignored or deleted, may or may not even get a canned response. I've heard state legislature staffers claim that they can get upwards of 10K emails a day about certain issues - there is simple no way they have the capacity to sort through them even if they wanted to.
Letter - a little better as someone actually has to open the letter and stick the form letter response into the envelope. At least the politician's staff get an idea of how many people are for or against an issue this way.
Phone call - even better. You talk to someone and are an actual person to them. In most cases they will claim to actually record a position (for or against) to be tallied for the politician.
In-person visit - best of all. Nothing gets the point across like crowding their office with bodies. In my experience you are unlikely to get to speak with the actual politician, who often will hide away from their office when contentious issues are up for vote so as not to interface with the public. Some are better than others here, obviously.
This is my experience only, perhaps you're politicians behave differently. But I am quite sure about one thing - sending email is a waste of time and gives you an easy excuse to think you've done your share. If you care enough to want to get in touch, at the very minimum pick up the phone and call.
ETA: I've also typically seen that regardless of the amount of pressure applied by the public for one side of an issue, nearly every politician will simply vote the party line anyways. They know where their bread is buttered, and won't go against party leadership. I've watched legislators look over at a senior party member and be signalled which way to vote when their turn comes up. I don't think anything I've done or said to my representatives has had the slightest impact on their opinion or voting record. That's just how the game is played.
I called my representatives and told them they got $2700 plus several days phone banking from me last election cycle. If they don't get right on this, they're getting $0 next time; I'm not going to have to work too hard to figure out something fun to waste a saved $3k on.
Oh, and if the above bothers you, support public funding of elections. He who pays the bills calls the shots, and all those companies profiting off surveilling the world make a lot of donations.