Q:

Why do we use single tape Turing machines for time complexity?

As you know there are many anomolies for the single tape Turing machines when the time is $o(n^2)$: multi-tape TM simulation, simulation of larger tape alphabet with just $\{0,1,b\}$, time constructability, non-tightness of time hierarchy theorem, ...
Also results like $\mathsf{DTime}(o(n\lg n)=\mathsf{Reg}$, and very model specific $O(n^2)$ time lowerbounds for simple problems (that don't translate to even superlinear lowerbounds on two tape TMs).
For space complexity, we use a model where we have a separate read only input tape, which is more natural and robust.
A TM model with multiple tapes (or at least 2 working tapes) would be much more robust and will not lead to anomalies like those I listed above. I once asked a prominent complexity theorist who has proven simulation results in the early years of complexity theory if he knows any improvements on one of these old results and the reply was that he doesn't think that "questions about the one tape model are that important".
If we change the standard model for time complexity to a two tape TMs, reasonable results in complexity theory will not change and we avoid these anomalies caused by particular model. So my question is:

is there any reason why the time complexity is still defined in terms of single tape TMs?
  (other than historical reasons) 

A:

I've seen texts define TIME( $f(n)$ ) using multi-tape Turing machines, but Sipser uses a single tape machine.  You've almost surely first encountered this material through Sipser because it's so fabulously well written.
There is a crystal clear pedagogical reason why Sipser does this, namely the course just naturally flows that way because :

You should introduce the single tape machine before the multi-tape machine, otherwise steepens the learning curve.
There is no compelling reason to introduce the multi-tape machine before introducing O($\cdot$) and TIME($\cdot$) for single tape machines.
You should ideally compare the multi-tape machine with the single tape machine the moment you introduce the multi-tape machine, otherwise the prolonged ignorance will lead to additional confusion.
You could omit introducing the analogous TIME classes for multi-tape machines, thus simplifying notation overall.

There is no reason to quibble over conceptual cleanliness when the pedagogy so clearly dictates the easiest path, and every computer science undergrad must take this elementary course, including all those who still don't understand proofs. 

A:

The other answers look very nice.  I'd like to share a comment Russell Impagliazzo made years ago in a lecture, which has stuck with me ever since.

I think Turing may have preferred a single tape TM due to physical plausibility.

I pointed Russell to this thread days ago but, seeing as he's not here, I'd like his comment known, and will do my best to interpret it.
For a single tape TM, supposing a tape of infinite length (please stick with me), you can build a TM which just needs a bounded amount of energy per iteration.  Imagine the tape as a long rod, and the head, which contains all TM logic, simply moves along this rod.  (I think of it as a cute little geared contraption, using very primitive technology.  The rod can have notches to help it along, and tape cell contents can just be a block slid orthogonally to the rod axis.)
On the other hand, how do you do this for a $k$-tape TM?  If you have $k$ of the above contraptions, they must communicate their read status to the potentially extremely distant other heads, which takes unbounded amounts of energy (say you use wires, which necessarily leak heat), and moreover is not instantaneous, thus complicating the mechanism.  If instead you kept the heads together and moved the tapes underneath them, you'd be using enough energy to move infinite-length tapes..  I don't see how to get bounded energy in either case.  Tricks like shrinking tape increments (to get finite length) suppose an infinitely divisible universe, and violate things like Planck's constant and the holographic principle.  Even ignoring these, the mechanisms in the head must be arbitrarily precise, which again causes energy problems, and is prodigiously complicated.
Of course, the first scheme has problems: the construction of the infinite tape with infinitely many notches, infinitely many suns to power solar collectors on the moving head, an infinite supply of cleaning and maintenance supplies, etc.  Maybe some major breakthrough in quantum mechanics can let the $k$-tape heads communicate well, but now look how complicated our contraption is.  In any case, I think Russell's comment is very, very interesting.

A:

The original Turing machine was described using a single tape:
www.cs.ox.ac.uk/activities/ieg/e-library/sources/tp2-ie.pdf
So as you state in your question, this is mainly for historical reasons. Furthermore, there is always the tendency to ask what is the simplest model that can do something...
Also, since this topic is usually being taught very formally, it is just technically easier to describe a single tape machine than a two tape maching.
See also:
http://www.cs.utah.edu/~draperg/cartoons/2005/turing.html

