Typically, garden asparagus (Asparagus officinalis) does not produce thorns on its lacy, wispy, arching branches as it matures over summer in the garden. The issue of thorns is more applicable to houseplants. Sprenger's emerald fern (A. densiflorus "Sprengeri"), climbing asparagus (A. scandens), common asparagus fern (A. setaceus) and Ming fern (A. macowanii) are among those species grown in containers as houseplants or outdoors in frost-free climates. These plants produce short, stubby thorns across the stems that are overlooked since the small and numerous leaves make the thorns difficult to see.
Thorns on the various fernlike asparagus plants serve two purposes. The first is protection. For species native to dry regions, where few other edible plants exist in the wild, the thorns serve to dissuade browsing animals from consuming them. Thorns also act as a support, like the spikes on mountain climbers' shoes. The long stems need to grow upward toward sunlight to compete with other vegetation. The thorns help anchor the stems as they elongate and flop. The thorns catch on other plant stems or trunks, allowing the asparagus to remain above shade.
While a warning about the presence of thorns on many species of asparagus is warranted, they are not dangerous in the sense of being poisonous or causing loss of limb or life from a prick. Puncture wounds from asparagus thorns get progressively more dangerous, however, if the wounds occur in an eye, for example. Falling into a thorny asparagus plant or thicket could be hazardous. The concern comes from the care of the wounds sustained by any thorns.
Any outdoor location, including a seemingly harmless, tidy garden, is filled with germs, bacteria and viruses. These pathogens can live on plants, in the soil or as airborne dust and debris particles. Gardeners are wise to maintain tetanus vaccinations, as this pathogen is widespread in garden settings, especially in soil. Any number of pathogens can live on asparagus thorns as they scrape or puncture your skin. Thoroughly wash cut areas with soap and water as well as a disinfectant such as hydrogen peroxide.