Cross-browser layout under which browsers?

Under what major browsers to make a site? Is there a stand-alone program for cross-browser testing, emulators (not online service)?

ps can you recommend a good online services (not just to preserve pictures), and you can see and climb on the site, emulating the right browser. Thx in advance and sorry for bad eng.

Basically a webmaster focus on mizilla, google chrome and IE 7,8 and higher… when lunching a new website, It’s a technical term 'browser compatibly. When you have building any website make sure your web designer have sufficient idea for the same, else the website may be working fine in IE and issue with mozilla or may be in chrome.

Realitypremedia, common ver Mozilla, chrome? What about Safari? What about mobile browser?