Seeds sprouting from last year

I've noticed this spring that there are a lot of sproutings of mint from seeds left from last falls mint plants.  The taste is a little bitter.  I also planted basil last year and saved some of the seeds as the plants died and dried out but none of the seeds from last years plants came up like the mint did. Should I pull the mint out, refresh the soil and then plant fresh seeds, or will the mint do well as it is?  Apparently the basil seeds that fell to the ground as the basil plants died off last fall will not come up this year.  (I did save many of the seeds - can I plant them this year?) Is there a general rule for herbs or more specifically, will most herbs go to seed at the end of the growing season, drop the seeds, and the seeds sprout in the spring?  Thank you.