I use Opera.
Annapurna, as long as you keep IE, windows, your anti-virus and firewall software fully up to date it should be fine. If you're only accessing safe, legal, well-known sites with good reputations all should be well.
There are no guaretees, of course, even with firefox or chrome or opera or anything else.
Edit for clarity: I use Opera Mobile. The advantage of using my mobile phone for all major intenet browsing is that most viruses and malware tend to be designed to attack windows, not symbian. The downside is that symbian is rarely updated on this handset and, if hacked, I could potentially get a very nasty phone bill. I'm protected by the credit agreement with the phone company though, so I think it's the lesser of two evils - if a hacker did seize control of my phone they couldn't do much with it... it's just not powerful enough