I've came across 「何度も」、「何度か」、「度々」、「しばしば」、「しきりに」、「よく」
First, there are two type of word that describe "frequency": one is to tell the occurrence is "fast", relatively many in a duration; the other, the accumulated (absolute) number is big. On this basis,
- 何度か: this means "a few/some/several times" instead of "frequent", that suggests the occurrence is low in number. = 何回か, 数度／回
- 何度も: close to "so many times", or the number is subjectively perceived high. = 何回も
- 度々: basically same to 何度も, but emphasizes that the same participant is involved or happens in their scope of interest e.g. 度々すみません "sorry to bother you over and over" (happens multiple times to the hearer). A formal/business-like word. = 再三, 重ね重ね
- しばしば: the observed frequency (number per duration) from third-party perspective is relatively high. You can refer to action of yourself too, but gives an impression being a reflective report. = ちょくちょく, ちょいちょい (colloquial)
- しきりに: "continually, repeatedly"; usually associated with anxiety when used on people e.g. しきりにこちらを気にする, しきりに顔を拭く. = しょっちゅう, 頻繁に
- よく: the most basic word for "frequently" (high number per duration), that suggests someone likes or likely does something e.g. よくある質問 "FAQ". Could be ambiguous with "thoroughly" sense of よく: よく洗う ("wash carefully"? "wash frequently"?).