There are many such tools, free and commercial. Here are some of the better-known ones.
Spoon.net
This browser sandbox supports Chrome 30, Firefox 24, Firefox Mobile 5,
Opera 16, Opera Mobile 12, Opera Mini 6, Safari 5, Internet Explorer 10
as well as many legacy browsers.
Browsers run within an isolated virtual environment, where
virtualized browsers behave exactly like installed browsers. Because they run locally, you can test web applications hosted on your own development machine or on internal servers.
Standard browser components are supported like Java applets and ActiveX controls as well as popular browser plugins like Firebug, IE Developer Toolbar, and CSS and JavaScript debugging consoles.
Browser Shots
If you have a website, you could use Browser Shots to obtain static screenshots
of a URL on up to 130 browsers, while also specifying the
screen size, color depth and the availability of JavaScript, Java and Flash.
Sauce Labs
Similar offering.
BrowserStack (commercial)
Instant access to 200+ desktop and mobile browsers on different Windows, Mac & mobile OS flavors. 3 months free testing.
Cross Browser Testing (commercial)
Similar offer, free 25 pages per month.
Browsera (commercial)
Similar offer, 30 days free trial.
Some Internet Explorer compatibility tools :
IETester (alpha release)
Utilu IE Collection
See this article for more :
Review Of Cross-Browser Testing Tools.