This is crazy weird. Guinness was one of the first beers that I tried when I started trying beers, and I loved it. I was going to recommend it to our OP except that he mentioned it.
Hi, Newbie Guest here. I also would suggest a wheat beer. Very cold with a slice of lemon or orange, on a hot day is perfection. My favorite is Hacker Pschorr, but Blue Moon does quite nicely as well.
I’ve yet to find a beer that I like; I drink cider, though.
Licking an ashtray? Try Guinness. 
Just popping back in to say that I have indeed tried hard cider before and love it. At least one particular brand of it (Woodchuck Draft Cider). I’m not sure what exactly it is I don’t like about beer, and it’s hard to say. But I’ll go pick up some of the beers everyone’s mentioned thus far and see if any tickle my fancy.
You’re recommending Bud and Natty Ice to someone looking to enjoy beer?! I think if the OP was so revolted by beer that only the most watered-down would be palatable, s/he would just not drink beer.
Zima, Smirnoff Ice, etc, and cider are not beer, nor do they resemble beer in any way except for marketing.
To the OP- if you’re looking around at your local supermarket, the beer section is usually divided into two not-always-obvious sections- one has Budweiser, Miller, etc. The other will likely have microbrews and maybe a few imports, many in six-packs. Avoid the former. Alos, avoid cans- the beer tends to taste metallic, and any beer in cans tends to be lower quality beer anyway.
My recommendation would be to try a hefeweisen (wheat beer) with a slice of lemon. They generally have the “heaviness” of a beer, but has a pretty mild, slightly citrus taste. If you find yourself at a brewery (a quick Google search shows several in Nashville), they often will offer a sampler- a handful of 3 oz glasses of their different brews. If you like any of them, ask the bartender what type of beer it is (pale ale, stout, IPA, etc), and what would be comparable to pick up at a store.
Whatever you end up with, pouring it into a glass lets you smell it as you drink this. I enjoy this, but you might want to drink it from the bottle… baby steps, baby steps… 
Bass and Harp are also good choices, and Sam Adams makes some decent stuff.
I’m not recommending this for a non-beer drinker, buy can’t resist mentioning that a “Black & Tan” with hard cider for the ‘tan’ is a very interesting drink. My favorite is Spire Mtn. Pear Cider, topped with Guinness. Sacrilege, I know, but it’s so tasty, and the appearance is very striking.
While cider is quite nice by itself, I don’t get how recommending it to Electronic Chaos is going to help with the beer issue. It’s not like cider is a “gateway” to other drinks…
Another way to make beer taste good is to be so thirsty that anything would taste good. I didn’t like beer either, until I discovered how refreshing it could be after a working in the hot sun all day. One summer working construction turned me into a lifelong beer drinker, and now I’m on the ‘hard stuff’ – Guinness or Murphy’s.
I disagree with the suggestion that one should start on beer “nearest water” to develop a taste for it. I could not stand Coors, Bud, Miller, etc., in high school and college, but my love for beer started when I had my first Samuel Adams lager.
Finally, a beer that tastes like something other than piss. Since then, my tastes have branched out to stronger and crazier beers (and I’ve come to appreciate the Budmilloors of the world, too), but forcing me to drink the typical American light adjunct lager was definitely NOT the way to do it for me.
I find it odd that so many people consider Guinness draft a strong flavor because, really, it’s rather mild and smooth. It just happens to be black, which I think throws a lot of people off.
I would say check out the Belgian beers. There’s something for everyone there. I don’t think there’s a soul in the world who doesn’t appreciate the occasional Kriek (sourcherry), Framboise (raspberry), or Peche (peach). They’re all sour-fermented beers called lambics, and don’t taste anything like beer, really. Look for the following brands: Drie Fonteinen, Hanssens, Liefmans, Lindemans, or Belle-Vue.
If you like truly really sour and stinky flavors, try a gueuze (unflavored, blended) lambic. Most people are not going to like this stuff, but I think it’s fantastic. If the taste of sparkling pickle/kraut juice sounds appealing to you, try Lindemann’s Guezue Cuvee Renee or Hanssens Oude Gueuze.
Also, give a try to some of the Belgian ales recommended. Everybody seems to like Chimay. If you can find Westvleteren #12, that’s often ranked as the best beer in the world. I’ve never had that one, but the #8, which also finishes in the Top 5 or 10 on most of these polls, is great.
Dogfish Head Raison D’Etre, which has been mentioned, is a domestic riff on the Belgian trappist ales. Definitely worth a try.
Heck, while we’re recommending Weizenbiers, why don’t we just head over the border for the Belgian take on it: the Witbier. These are a bit different than they’re German cousins. They’re usually flavored with coriander and curacao orange peel and have a very distinct, spicy bite to them. Hoegaarden is the quintessential brewer of this style. Try it.
For more typical beer tastes, but with more flavor, try something like a Czech Pilsner Urqell or Staropramen. They’re especially perfect for this time of year.
The other beverages are often consumed in similar situations as beer. Whether watching a tv at home at night, or drinking socially at a bar or party, hard cider (or, Zima :blech: ) fills the same niche. The difference between a Bud and a Guiness is certainly as much as the the difference between them and a Woodchuck, the “beer” label, notwithstanding.
Troy, never mention cider and Zima in the same sentence, please! Cider certainly has a place in the world; Zima is illegal under the Geneva Convention.
Daniel
I’d love to try more of the Belgian ales, myself. One of my favorites is Delerium Nocturnum, which comes in a large tan ceramic bottle (like a wine bottle), with a blue foil sticker with a pink elephant on it. It’s dark (but not as dark as Guinness) and has a nice sweet flavor.
I gotta agree with LB here. If a person doesn’t really like beer but wants to develop a taste, you can’t send them to the heavy stuff first.
It’s gotta be gradual. When you are learning to play guitar, they start you out with “Frere Jacques” not “Sweet Child O’Mine”!
I was gonna recommend Ultra myself. I enjoy it, as it is a very “aquatic” beer. Danalan’s pitch of the Silver Bullet as an intro beer is also on base.
But some of the heavier beers are WAY to strong for a newbie.
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Did anyone ever participate in the Bennigan’s Beers of the World promotion? Basically, they had over a hundred beers at the bar. You signed up for a card with a magnetic strip that kept track of your purchases. Every day, you could add four new beers (limited to four for liability purposes). If you got 100, you got your name etched on the bar.
I made an effort to complete it, but moved away before I could get pass 80. My new town did not have a Bennigan’s.
Let me just say. There are a lot of good beers and a lot of BAD beers in the world.
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I am not a big beer fan.
The the really cheap beers ( Red, white & blue & Pabst Blue Ribbon) were the only ones for a long time I liked. (I switched to hard stuff after those preliminary years of bad taste.)
I do like Astra which is a Urtyp beer from Germany. I know Urtyp is a kind of beer, but I don’t know what it means. And I only remember this because I have a intact label I peeled off. 
I am sure there is someone here can tell me what that means.
Interesting that nobody has mentioned Newcastle. I know quite a few people, myself included, that didn’t like beer until they tried NC. Maybe it is the slightly sweet flavor and mild aftertaste. All I know is that it was the first beer that held any appeal to me and gave me an understanding of the difference between a decent beer and that domestic piss-water. And in time, I moved on from Newcastle, prefering IPA’s and stouts. I don’t think I ever would have though, had I only tried Bud and Coors.
If anyone knows where or how I can pick up a case of Astra or Jever in the states, or even Ontario, I’d appreciate it.
Hey, there’s nothing wrong with PABST BLUE RIBBON! I consider myself a fan of “nice beers,” but something about the PBR always draws me in. It’s mighty tasty compared to any other cheap, light American beers.
August West already mentioned Lindemanns, but I’ll second that recommendation. The lambic Frambois (sp?) is fantastic, and doesn’t taste like beer at all. It’s like a very tasty fruit soda, but more complex than sodas. It is much better than those horrible flavored “malt beverages.”
Really, you should give it a try.
Is ok to admit publically that I also drank Old Milwaukee?
Cause I was young, naive and broke. (Woooo a trifecta!)
I’m not huge on beer, but I like a nice cold Rolling Rock. It’s the only beer I can drink straight - meaning without eating some sort of food product.
I tasted a lovely chocolate beer at a Boston brewery once. I coulda drank that one… with food.