I'm on Day 102 of a low carb diet (more or less Atkins) and am so far down almost 3 stone :) I never feel hungry, and I get to eat some wonderful food - eggs and bacon for breakfast, salmon with Hollandaise and a big salad, even Coq au Vin (red wine isn't that high in carbs), chilli con carne minus the beans, roast pork belly, including the wonderful crackling, roast chicken with the skin on, veggies like courgettes cooked with garlic and butter, or mashed cauliflower with cream cheese. I allow myself a few higher carb veggies like onions and maybe a carrot from time to time, but never eat potatoes.
Eating out is easy - burger without the bun or a steak (smothered in garlic butter) and salad, or a Sunday roast without the spuds and Yorkies. I can even do Indian restaurants if I stick to he tikka/tandoori stuff. Chinese restaurants are a challenge, it must be said!
Because I'm not hungry, I rarely eat snacks, but if I ever get a bit peckish, then I snack on Babybels, Brazil nuts, Peperamis, or hardboiled eggs. Also, I rarely eat sweet stuff, but if I get the urge, I'll have a few berries (black, straw, rasp or blue) with a generous dollop of extra thick double cream.
Gary Taubes 'Why We Get Fat' is worth a read if you're interested in how a low carb diet works to combat hunger, and why you lose weight more or less effortlessly when eating this way. The science makes sense.
I've done SO many low fat/low cal diets over the decades, and always found them to be an exercise in willpower - which in my case always fails in the end! The first couple of weeks low carbing can be difficult - before you've lost the sugar cravings and you body's moved into fat-burning mode, but it is really worth white-knuckling it through them - right now I'm coasting along happily and enjoying every minute of this way of eating.
It's not too difficult to eat low carb whilst the rest of the family eats normally, either, you just add a portion of carbs (pasta, rice, spuds) to whatever you're having. Shredded lettuce makes a good substiute for pasta, btw.
I just wish I'd known about low carb 30 years ago, but I bought into the whole low fat thing and spent years beating myself up for lacking the willpower to stick to an allegedly 'healthy' way of eating. Now I know better :)