Read our full review of Catan HD for iPad for more information, but here's the gist: it's a decent adaption of a superb board game, much faster-moving because the iPad works out all the victory points for you, and a bargain at £2.99, and £2.99 per expansion. (Seafarers is wonderful, Cities & Knights less so but still an excellent introduction to that expansion's more complicated rules.)
The computer players are much more vicious than real-life players, but that shouldn't affect a family game.
If you want something gentle for a kid-heavy gathering: Ticket to Ride (£4.99)
Hardcore fans may disagree, but our experience suggests there isn't enormous tactical depth to Ticket To Ride, but it's fun and gentle enough for both the relatively young and the extremely hungover to join in. Essentially you pick up cards that let you play various kinds of railway rolling stock, and use these to build a rail network that connects enough points on the map to fulfil the various missions you're given.
If you're ready for something with real complexity and a touch of humour: Small World (£4.99)
Our games editor tried to get this classic included in our recent '50 best iOS games' feature, but got outvoted by the rest of the team. We've all been playing it heavily since, however, and it may well make the list next time.
Small World is set in a Tolkien-esque fantasy universe with a facetious flavour. Your aim is to amass victory points by conquering and holding tiles on the map, but there are numerous special rules that affect this, depending on the race of characters you select at various points in the game, and the special ability which has been randomly assigned to them for that game only.
The combinations of races and abilities are huge so no two games turn out alike. And the brevity of each game (not to mention the back-and-forth flow of almost every skirmish) means there's none of that gradual sinking feeling you get for the last two hours of a game of Risk where you know the end is coming. It's only two-player, sadly (the board game allows up to 5). We hope this is addressed in future.