I am working on a project which requires IE6 compatibility. Unfortunately, IE6 and IE7 do not support standards mode. Because of this, I am tempted target almost standards in for all browsers and just ignore standards mode completely, so that I am only targeting browsers running in the same standards mode. I figure that because XHTML transitional is so popular, almost standards most is guaranteed to be supported for a long time to come. Is this a good idea?
No, this is not a good idea.
Its not a good idea because eventually IE6 will be obsolete (sooner rather than later) and you will have a messed up site where you have to jump through hoops to get it to look halfway decent.
A better solution is to use progressive enhancement, in a nutshell support the minimum you need for IE6 and give the modern standards following browsers the goodies.
With progressive enhancement you still get your support for IE6 but you're left with a standards based website that is easier to maintain and develop further.
Using "almost standards" mode is dumbing down other browsers for the sake of IE. IE6/7 doesn't support a standards mode because it's incompetent. You should never write markup aiming at incompetence. Write modern markup with a strict doctype and use "conditional comments" to hack and beat IE into the best compliance you can get out of that thing or you will be doomed to a world of darkness and hurt.
Roughly 40% of the user base of my company's software uses IE6 (down from ~60% a couple years ago).
Our master pages have the XHTML 1.1 doctype set. I do all my design work using the latest version of Firefox and then once I have it all working how I want, I test in IE6 using the App Compatibility VMs for Virtual PC that MS releases, and make any necessary changes to my CSS that IE6 requires.
Most of the time I can just use slightly different CSS and don't have to resort to hacks, although sometimes I still do. But the hacks don't affect other browsers, since they're IE6 specific. I haven't gone to the length of using browser-specific CSS files yet, cause the extent of my IE6 hacks are something on the order of 10 lines out of ~1500 lines of CSS. My modified CSS to "support" IE6 still renders fully standards-compliant in Firefox.
EDIT: thanks to Rob's comment I'll be changing my doctype to "HTML 4.01 Strict with system identifier" (provided testing shows that it doesn't break anything). That Quirks Mode chart on Wikipedia shows my current doctype (XHTML 1.1 with system identifier and without XML declaration) results in the same render modes.
Everything I said above still applies, though. I code for standards-compliance in the latest version of Firefox (the Web Developer add-on is my friend) and then "make IE work" without breaking standards-compliance in Firefox.