I know dubbels are considered as strong beers, but what should I expect in when I try one of them?
What are their defining characteristic? What should I expect in term of taste, foam, color and mouthfeel?
As with any style, there's a fair deal of variation from one brewery to another. At a high level, though, you can expect them to be darker (although not stout-dark), rich, and malty. Expect a complex taste, with many notes and flavors.
More specifically, the BJCP have this to say (abridged):
See here for the full description.
A Belgian Double is an amber/brown beer of usually 6-7.5% ABV (They can drift higher). The style was most likely originated at Westmalle in the mid 19th Century. While Trappist abbeys tend to be the origin and driver of the style, many secular Belgian breweries produce them as Abbey beers which may have actually been a brewing monastery at one point or simply as a Dubbel. They're not as popular amongst American brewers as triples though.
As far as flavor profile, it's a malty but dry beer. The Belgian abbey yeast strains will ferment the beer fairly dry but will create a whole host of fruity esters and spicy phenols that will add to the mid range caramel malts. Many of the Trappist versions have attenuation of 80%-90%. Westmalle Dubbel, Chimay Red Label, New Belgium Abbey, St. Martin Brune are all good examples of the style.
With regards to AudiFanatic's answer, In this case, Beer Advocate is wrong in their description of a Triple. Triples do NOT use 3x's the malt as a Single. No brewer will tell you that, nor is it true historically. Malt extraction is linear, meaning 3x's the malt will be 3x's the alcohol. The closest you get to that is historically when the single was the 3rd running (like a small beer). With this method, the 1st run had triple the fermentables extracted than the 3rd run.
And while I may only be a blogger, with 13 years of industry experience, I spoke with highly trained brewmasters and read references written by authoritative experts. I'm pretty sure my answer article is more accurate than the Beer Advocate's, in this case. Also, the flavor profile of a triple does not have "flavors similar" to a dubbel. Dark malt and light malt will give very different flavors. The only Triple that has similar flavor is Stift Engelzell's triple, which is a unique dark triple, as they're labeling it.
In short, prepare for a hangover. They pack a strong amount of alcohol (6-9% ABV), but you won't really taste it much. You're gonna get a lot of malt flavor, they're not very hoppy beers. So expect some sweet, fruity flavors. I'd recommend you give Allagash Dubbel Ale a try. It's a bit pricey (at like $12 for a 4-pack), but it's well worth it. I've never been disappointed by any beer from Allagash.
Now If you're curious, a Tripel is like a double, but they use three times the amount of malt than a standard Trappist "single", hence the name. So expect flavors similar to that of the dubbel, but much more pronounced. They are also higher in alcohol than a dubbel (9-12% ABV). For this style, my personal favorite, as of now (I've only had two of them) is Weyerbacher Brewing Co's Merry Monks Ale. The other one was the Allagash Tripel, which was also outstanding, but I'm partial to the Monks.