We present Xspect, a method to obtain estimates of the angular power spectrum of the cosmic microwave background (CMB) temperature anisotropies including analytical error bars developed for the Archeops experiment. Cross-power spectra are computed from a set of maps and each of them is in itself an unbiased estimate of the power spectrum as long as the detector noises are uncorrelated. Then, the cross-power spectra are combined into a final temperature power spectrum with error bars analytically derived from the cross-correlation matrix. This method presents three main useful properties: (1) no estimation of the noise power spectrum is needed; (2) complex weighting schemes including sky covering and map noise properties can be easily taken into account, and corrected for, for each input map; and (3) error bars are quickly computed analytically from the data themselves with no Monte Carlo simulations involved. Xspect also permits the study of common fluctuations between maps from different sky surveys such as CMB, Sunyaev-Zel'dovich effect or mass fluctuations from weak lensing observations.