If you like herbs like we like herbs, then you plow through more than the average American. There are also likely fresh favorites you keep around pretty much all the time. For us, that would include cilantro and parsley. Both have subtle, lovely flavor profiles that go great with many dishes.
That said, both can get long in the tooth quite quickly. They're highly perishable, and can be hard to keep fresh after even a couple of days in your fridge. Considering the handling such foods receive as a part of modern distribution and sales, it's no wonder, really. A little handling and preserving work can go a long way toward having these indispensable always at hand.
When you get delicate perishables home, inspect them first and foremost. Get them out of the plastic produce bags, and better yet, don't put them in those things in the first place and reduce your plastic throughput. Remove any off colored or bruised stuff and toss it in your compost.
Give your goods a gentle rinse in cold, running water. Shake them dry, gently but thoroughly; excess water is not a friend to successful storage.
Remove any rubber bands or twist ties; all they do is bruise the goods and promote rot.
Place the washed produce on a clean paper towel and let them air dry a bit. Wrap the goods in the paper towel and store them in your crisper drawer just like that. If you use what you buy steadily, and pay attention to FIFO, (First In, First Out), in your fridge, your cilantro, parsley, green onions, radishes, etc will stay fresher, longer.
Consider drying some of those staple fresh herbs. It's a given that fresh is better than dry, but house dried herbs from a good fresh source are far better than store bought or none. Those faves of ours will dry thoroughly in a dehydrator in less than 30 minutes. I've tested both cilantro and parsley and found that our home dried stuff retains reasonably potent flavor for up to a month when stored in glass, in a cool, dark, dry spice cabinet.
Finally, and especially as the winter months are upon us, plant a fresh herb window box. An 18″ x 6″ x 6″ box will allow you to grow a full raft of your faves, and reasonable tending will sustain them through the season. There's nothing cheerier in the dark months than fresh, bright herbs growing in your kitchen.