Rateless codes have been shown to provide robust error correction over a wide range of binary and noisy channels. Using a stochastic geometry model, this paper studies the performance of rateless codes in the cellular downlink and compares it with the performance of fixed-rate codes. For the case of Rayleigh fading, an accurate approximation is proposed for the distribution of the packet transmission time of $K$-bit information packets using rateless codes. The two types of channel coding schemes are compared by evaluating the typical user and per-user success probability and the rate. Based on both the analytical results and simulations, the paper shows that rateless coding provides a significant throughput gain relative to fixed-rate coding. Moreover the benefit is not restricted to the typical user but applies to all users in the cellular network.