One of the "reproducibility" issues that has come up with the various recent projects that have made the news is that many old studies no longer have legible, accessible, or ANY lab notes or data. Lost or spoiled paper notebooks and files, outdated file formats or corrupted disks, or changes to procedure or analysis that were never documented in the first place can make your work non-reproducible.
The best digital lab notebooks, also known as Electronic Lab Notebooks (ELNs), combine the ease of a paper notebook with the ease of backup and transfer of a digital tool. The important part is making the notetaking as easy as possible so you don't forget to do it! Good digital tools also can be shared across the lab, so everyone is kept aware of procedures, and changes.
There are commercial ELNs, as well as more general purpose notetaking tools, some of which are free. Other options might include a digital camera or video camera, voice recorder, and various tablets or similar devices to make the system as portable as possible. The following are a series of articles describing various researchers experiences with a variety of tools.
Probably the best advice is to ask colleagues with similar labs and workflows what they are using.
Be sure to back up or archive your notebook frequently. Procedures and lab notes can be published, like data, as supplementary resources along with a published article.
Publication bias, or "the file drawer problem" is well known: generally, only successful studies are published. Traditional publishing doesn't reward negative results, but science depends on knowing what's been tried. The medical field has adopted Clinical Trial Registration as the standard, saying that all clinical trials should be registered and some report made of the findings no matter what the outcome. Both experimental and observational studies can be registered at ClinicalTrials.gov.
Other fields are considering the same sort of recommendation (Psychology, here and here, Economics, Political Science, Development, ), and some researchers have voluntarily dug their results "out of the file drawer" and published the results in open repositories.