It is possible to employ a method presented in Transformation of quantum states using uniformly controlled rotations. The article shows (besides) how to implement gate controlled by $n$ qubits and yielding a state
$$
|\psi\rangle_{n+1} = |i\rangle_{n}\Big(\sqrt{1-f(i)}|0\rangle + \sqrt{f(i)}|1\rangle\Big),
$$
where $i$ is a binary representation of $n$ bits number and $f(i)$ is an arbitrary function. Setting function $f(i) = 1$ for $|i\rangle = |1 \dots1\rangle$ and $f(i) = 0$ otherwise allows to construct Toffoli gate with as many input qubits as one wants without ancilla qubits. Note however, that increase in number of gates is exponential in number of input qubits. For $n$ input qubits $2^n$ $CNOT$s and $Ry$ rotations is used.
However, in comparison with complexity of circuits used for implementation of Toffoli gate on IBM Q, the circuit is simpler. In case of two qubits, four $CNOT$s and four $Ry$ gates are used (note that after transpiling the circuit on IBM Q, $Ry$ are replaced by $U3$ gates).
A implementation of Toffoli gate with above mentioned method is this:
Note: Parameter $\theta$ is set to $\pm\frac{\pi}{4}$.
I tested the new gate "abilities" on input $|11\rangle$. Backend ibmqx2 was used, number of shots was set to 8,192. The circuit was designed to follow the backend physical implementation and hence to avoid qubits swaps after transpiling. A probability of measuring $|1\rangle$ was 93.286 %, while the same probability with Toffoli implemented on IBM Q was 87.486 %. Clearly, simpler circuits helped to get a more coherent results.
The method also allows to implement Toffoli gate with three inputs:
Note: Parameter $\theta$ is set to $\pm\frac{\pi}{8}$.
I again tested the circuit on ibmqx2 with same setting as above and compared it with Toffoli gate on IBM Q (here I had to use ancilla qubit and three two input Toffoli gates - one for uncomputing the ancilla). Input of circuit was $|111\rangle$.
A probability of measuring $|1\rangle$ was 81.213 %, while the probability with Toffoli implemented on IBM Q was 30.542 %. This means that output of construction with two inputs Toffoli gate and one ancilla qubit is very decoherent.
EDIT: based on DaftWullie comment.
Actually above introduced simplification of a Toffoli gate can be used only in case qubit $q_2$ (or $q_3$ in case of three inputs) is set to $|0\rangle$, i.e. the gate operate as AND known from classical Boolean logic. The reason is that a matrix describing circuit above is
$$
\begin{pmatrix}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\
0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
\end{pmatrix}
$$
This means that for input $|111\rangle$ a phase is shifted by $\pi$.
As a result, the circuit is not "general Toffoli" and can be used only in special cases where it is ensured that the "last" qubit is set to $|0\rangle$
