First off, I would highly recommend trading up into a Camry from your Corolla. My gf's aunt has an '06 Corolla and the Camry is just so much nicer. Not everyone needs or wants a larger car, or cares much beyond reliability, but the Camry rides nicer, handles better, and feels more solid.
Are you talking about a new or used car?
If you're looking for a used one, you can't go wrong with any model camry made before 2007 model year. Personally i'd avoid the 2007, 2008, and 2009 Camry models. These cars were a major redesign and just by looking at a lot of posts on this forum, they have had big problems with the brake systems, the "drive by wire" steering, and several other items. Consumer reports dropped Camry off the "best buys" list for those model years (although the 2010 and newer may be better since they put it back on the list, but thats all i know).
If you intend to buy a used V6 (older then 2007 model year), beware of sludging issues. These were the engines (1FMZE) that were involved in the sludging recall. If they had their oil changed at every 3,000 miles the engines were fine, if the owner ignored the oil changes the engines could be sludged badly.
Personally i own a 2002 V6 with 145,000 miles and it's been the best car i've ever owned.
If you find a decent camry i'd say go ahead and buy it after checking it out, a Camry is usually one of the most reliable used cars you can buy.
I disagree. The gen 6 has had its share of problems but that's what happens during a complete redesign, though it was worse because Toyota cut costs too much. Plus - most people come on the forums to complain. Not nearly as many will come on here simply to say how much they love their car.
My gf picked up an '09 Camry I4 in June and has put 4K miles on it since then. It's got a few rattles but it is mechanically sound. I am VERY picky but I've driven her car extensively and it handles and drives well. They also improved NVH. I'm impressed. I would and am seriously considering getting into a newer Camry. I'll probably wait til the 2010s hit the market used as I want VSC+TRAC. I'm debating on whether or not to gamble with the new 2.5L I4 because the (now ancient) 2.4L I4 had problems with head bolts stripping with early builds.
I am particularly fond of the gen 5 Camrys (2002-2006) as I own one, and would highly recommend them. If you want an I4, go for 2005 and newer. The V6 is a great engine but if you're looking for economical, labor will always be cheaper on the I4.
We'll see what I end up doing in the next year or two.. I told myself I'd find something more interesting (e.g. not another Camry) but it's got all the features I like and the ride is comfortable. Optiron gauges, auto lights, and a power driver's seat has been standard on the Camry LE for years; it's hard to find some of that on the lower trim models on the Altima, Legacy, and 6!