This is not an exhaustive list, just the most popular awards in amateur radio.

ARRL Awards
DXCC (DX Century Club)
Worked all States – US
Worked All States – US (CW, SSB, Digital)
Worked All Continents
Worked All Prefixes
VUCC (VHF/UHF Century Club)

CQ Awards
USA Counties Award

AMSAT Awards

POTA (Parks on the Air) Awards

SKCC (Straight Key Century Club) Awards

Ten-Ten Awards

JARL (Japan Amateur Radio League) Awards
These awards are not common because they are manually tracked via a spreadsheet. You can also only use printed eQSLs and physical QSL cards to apply. Highly recommend using the QSL bureau for these awards.
AJA
JCC
Century Gun Award

Each organization accepts different confirmations. Check out the page: Which electronic QSL site should I use to confirm contacts?