Coriander (Cilantro) Going Downhill

My coriander is growing white flowers at the top; do I trim them off? They are going a bit downhill.

Coriander or cilantro (Coriandrum sativum) does not produce many useable leaves once it starts to flower and set seeds. This is the main problem with coriander – it wants to put all its resources into reproducing itself but we want leaves. Removing the flowers may help delay the inevitable decline of the plant somewhat, but sooner than we'd like it will come to the end of its useful life.
There are several approaches to solving this problem. One is simply to to reseed coriander repeatedly through the growing season so you always have some juvenile plants with an abundance of leaves. Another partial solution is to plant the slow bolting varieties such as 'Santo', however, they too will go to seed eventually. Or, plant Vietnamese coriander which never flowers and nevers goes to seed. Vietnamese coriander is not exactly equivalent to fresh coriander, but for many it is close enough.