Is there a way to run IE6, IE7, IE8 at same time or one after the other, to test UI of a web application. Or is there any other solution for this.
Use IETester - it allows you to test your site on all versions of IE.
In addition to the already posted IE Tester, there are tools like browsershots.org out there to test the look and such and Microsoft's Super Preview (part of Expression), but no way to have them completely installed side-by-side (like a normal client would) that's not complete hackery, at least that I'm aware of.
Although IETester can be useful at times, it does sometime render content slightly different and some JS scripts might not work as they would on the real thing.
So in my experience it's best to setup some virtual machines which has a different IE version on each instance.
I know this might sound tedious, but in the long run it's better to test and verify your websites that way.
You can do this using 'XP mode' in windows 7 - you need two virtual hard drives set up, but you can then create shortcuts on your win 7 desktop to 'open' IE6. There's a good walkthrough of how to do this here:
http://articles.sitepoint.com/article/ie6-ie7-ie8-win7-xp-mode/1
Virtual PC with multiple virtual machines, each with a different version of IE.
Microsoft even makes Windows XP/Vista + IE6/7/8 VM's available to download here.
I have used IEtester etc in the past. but for me there is no better alternative than viewing the applicationd in VM's set up as possible client setups. IETester is good, but I found that not all script issues were necessarily raised or reported. So in the interest in being thorough the VM solution is the best.
@Esko - surprisingly there are still a number of organisations who have standardised on IE6 and won't allow upgrades, as they still have legacy applications running that still require IE6. strange but very true :-)
You can also try Adobe® BrowserLab, I have used it to test with many browsers instead of installing them. Not the best but since all the others that I know of have already been mentioned, just another alternative.