Most of the drugs being trialed are repurposed drugs, so we can't expect miracles. Scant evidence (at least until the trials end) say that giving them early on may lead to better response.
Currently, there are a number being tested by WHO and other trials, I list the ones that come to mind:
- remedisivir (repurposed anti-Ebola drug): several trials to end by May-June
- lopinavir/ritonavir (anti-HIV drugs): those delivered bad results in a recent study, but those so far were (a limitation noted by the study authors) on patients with rather severe sympthoms, so it's still undecided whether they're effective or not
- Chloroquine family (chloroquine/hydroxychloroquine, with or without azithromycin): some preliminary studies may have shown interesting effects, but there were small sample sizes (also in another study which apparently was not very successful). U of Minnesota started a largish (3000 people) trial to see if it's prophylactic for immediate post-exposure to the virus. Another one started a couple of days ago to test the combination with the antibiotic (whose reported purpose is to fight off secondary infections)
There are others with less spotlight such as favipiravir, which provided a (modest) improvement in a small trial in China, and it's now part of a Phase 3 trial in Japan, or whole classes of drugs to combat the secondary but clinically important sympthoms like overinflammation (which occurs in some patients) like tocilizumab.
A lot of eyes are pointed on the chloroquines because they are already available (although they do present significant side-effects).
Neither of these drugs (or many others, see for example https://biocentury.com/coronavirus for some lists) will likely provide miracles. What the trials will do (hopefully!) is to help understanding how early they must be taken, and how effective they are in clinical management. An advantage, however, is that they will be available faster than a vaccine (modulo some non trivial issues like mass production).