The webblog lingutools (only available in German) offers a comprehensible overview of common tools for linguistic annotation and corpus analysis. It also lists possible advantages and disadvantages of these tools.
EXMARaLDA and ELAN (both freeware for Windows, Mac and Linux) allow detailed transcription and (also complex) annotation of audio and video files. Both are especially suitable for detailed analyses of linguistic and other behavior.
BORIS (freeware for Windows, Mac and Linux) allows annotation and analysis of video files.
f4 or f5 (paid software for Windows, Mac and Linux) allows for relatively easy transcription of audio and video files. This software is particularly suitable for content analyses.
Praat (freeware for Windows, Mac and Linux) enables detailed (phonetic) analysis and annotation of audio files.
R, JASP (both freeware for Windows, Mac and Linux) and SPSS (paid software for Windows, Mac and Linux, UPB students can get campus licenses allow detailed statistical analysis of quantitative data.
For purely descriptive statistics, Excel (available via campus license for UPB members) or well-known freeware alternatives are also suitable.
MAXQDA is a paid annotation software for qualitative data analysis.
CLARIN-D is a digital research infrastructure software for language resources in the fields of humanities and social sciences. It offers various (i.a.) tools for analyzing language data.