Read alignment is an ongoing challenge for the analysis of data from sequencing technologies. This article proposes an elegantly simple multi-seed strategy, called seed-and-vote, for mapping reads to a reference genome. The new strategy chooses the mapped genomic location for the read directly from the seeds. It uses a relatively large number of short seeds (called subreads) extracted from each read and allows all the seeds to vote on the optimal location. When the read length is <160 bp, overlapping subreads are used. More conventional alignment algorithms are then used to fill in detailed mismatch and indel information between the subreads that make up the winning voting block. The strategy is fast because the overall genomic location has already been chosen before the detailed alignment is done. It is sensitive because no individual subread is required to map exactly, nor are individual subreads constrained to map close by other subreads. It is accurate because the final location must be supported by several different subreads. The strategy extends easily to find exon junctions, by locating reads that contain sets of subreads mapping to different exons of the same gene. It scales up efficiently for longer reads.