What are browser bugs that are obscure in the sense that they are hard to find or only occur under certain conditions, but can seriously bite you? Please also provide fixes or workarounds where available.
Things like the IE6 float margin or PNG bugs are well known by now, please concentrate on rarer problems.
This is a community wiki, so please feel free to edit answers to make them more specific or accurate or to add solutions. One problem and solution at a time please.
When serving documents as XHTML, Internet Explorer 7 and 8 may display a blank page.
This can happen if IE tries to display the page using the wrong encoding. That even means the page may display correctly in IE on one computer, but fails on another if the default encoding settings differ. Just specifying the encoding using meta tags in the document itself is not enough in this case, since IE may (wrongly) guess the encoding before reading the tags.
Solution:
Make sure to use the appropriate HTTP Content-Type header, like:
Content-Type: text/html; charset=UTF-8
An embedded swf will not load in firefox if placed in a div of 0 width or height. It WILL load in other browsers, but you may set the width or height to 1px to force loading across all browsers.
One that I came across recently: IIRC it affects IE and Firefox but not Chrome. Haven't tested it elsewhere.
If you have a cell (<td>) that is supposed to have a border, the border won't show up if the cell is empty. Put a " " in the cell and it's fixed.