What are the most common font-sizes for H1-H6 tags
Headings are normally bold-faced; that has been turned off for this demonstration of size correspondence. MSIE and Opera interpret these sizes the same, but note that Gecko browsers and Chrome interpret Heading 6 as 11 pixels instead of 10 pixels/font size 1, and Heading 3 as 19 pixels instead of 18 pixels/font size 4 (though it's difficult to tell the difference even in a direct comparison and impossible in use). It seems Gecko also limits text to no smaller than 10 pixels.
It would depend on the browser's default stylesheet. You can view an (unofficial) table of CSS2.1 User Agent stylesheet defaults here.
Based on the page listed above, the default sizes look something like this:
IE7 IE8 FF2 FF3 Opera Safari 3.1
H1 24pt 2em 32px 32px 32px 32px
H2 18pt 1.5em 24px 24px 24px 24px
H3 13.55pt 1.17em 18.7333px 18.7167px 18px 19px
H4 n/a n/a n/a n/a n/a n/a
H5 10pt 0.83em 13.2667px 13.2833px 13px 13px
H6 7.55pt 0.67em 10.7333px 10.7167px 10px 11px
Nowadays, all modern browsers have the same values as defaults.