Hi Peter, some comments

> The total time to be checked is 5 years and the resolution has to be 1
> minute.

You simply won't get that accuracy over 5 years with a PIC's TMR. An
external timing source is needed

> Now first the task is very simple: When the PIC (I intend to use a
> 12F629) is powered up, it reads the already elapsed time from
> EEPROM, then simply starts to count minutes (by TMR1 and an
> added software divider) and when a minute is over it stores the new
> total time into EEPROM.

What about partial minutes ? If power-up/power-down is frequent
you'll lose a lot of combined time. Which affects the above accuracy
of course

> Now the problem is, when calculating the total number of storages
> you'll get 5 years x 365 days x 24 hours x 60 minutes = about 2,6
> x 10E6 write cycles, but the spec only says 10E6 cycles for
> EEPROM memory.

See the thread
[PIC] Count 20M+ in EEPROM counter

from mid-January 2006

You might want to consider not writing to EEPROM every minute but
holding the PIC's Vcc for a while up with a cap after power-down so
that the most recent value (stored in RAM) can be written

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