Formatting a hard drive is a necessary process to "initialise it" and be able to use it for the first time as a user. So, no it is not affecting its lifespan. If formatting for the first time i suggest using a full format (not quick) so that the disk can detect and flag any bad sectors out.
Also reformating a HD does not have any material affect on its life.
However, solid state disc drives are different - and that is what you may have been thinking about. Since ssds essentially have a limited number of write cycles, reformating wears them out more quickly, but I think the difference is fairly small for just one or a few writes.
I do not think there is solid evidence that formatting a hard drive often reduces its lifespan by much and i would not think so. The only real downtime i see in that is the loss of the user's time doing that. Why would you format your HD so much? lol
raijen, are you sure you are not confusing formatting with defragmenting?
Reformating completely removes all software. Do you reload your OS and all applications 10 times a week?
And if it is defragging - why do that so much? What percentage of your files are fragmented each time before you defrag?