If you are an amateur designer or if you do it as a hobby, then you have to have as a reference the professionals of the sector. They are people who spend hours in this and who know very well what they do and what they use.
After the jump I leave you the 22 most used fonts by professional developers, which means that we are dealing with good quality sources, valid for many types of project and ready to use.
I highly recommend taking a look at them, you may have many, but if you only need one it will be worth it.
Source | css blog
1. Delicious
Official download link: Click here
2. gentium
Official download link: Click here
3. tallies
Official download link: Click here
4. Lido STF
Official download link: Click here
5. MgOpen
5(a). MgOpenCanonica
Official download link: Click here
5(b). MgOpenCosmetics
Official download link: Click here
5(c). MgOpenModata
Official download link: Click here
5 d). MgOpenModern
Official download link: Click here
6. Thistle
Official download link: Click here
7. Day roman
Official download link: Click here
8. Yanone coffee grounds
Official download link: Click here
9. Union
Official download link: Click here
10. Fontin family
10(a). The font
Official download link: Click here
10(b). Fontin sans
Official download link: Click here
11. Fertig Pro
Official download link: Click here
12. Droid Font Family
Official download link: Click here
13. M + Outline Family
13(a). M + Outline 1C
Official download link: Click here
13(b). M + Outline 1M
Official download link: Click here
13(c). M + Outline 1P
Official download link: Click here
13 d). M + Outline 2P
Official download link: Click here
14. Luxi family
14(a). Luxi Monkey
Official download link: Click here or download using OpenOffice.org's FontOOo wizard.
14(b). Luxi sans
Official download link: Click here or download using OpenOffice.org's FontOOo wizard.
14(c). Luxi Serif
Official download link: Click here or download using OpenOffice.org's FontOOo wizard.
15. Ambrosia
Official download link: Click here
16. The cradle
Official download link: Click here
17. Liberation Family
17(a). Liberation sans
Official download link: Click here
17(b). Release Serif
Official download link: Click here
18. Advent Pro
Official download link: Click here
19. ATF Antique
Official download link: Click here
20. Mank sans
Official download link: Click here
21. devil
Official download link: Click here
22. Cycle
Just to say that it seems to me a great compilation of types, but you have not pointed out a detail that they are the most used free. I think it is important to highlight that point since I do not believe that they are neither in quality nor in quantity of use above other types of payment.