Methods of dealing with cursing attacks:
1. Give them out first. With rare exception, a curse your opponent gives is unlikely to end up in your deck. This is always an option and sometimes the most effective option is to win the curse war.
2. Trash them. This can be done with simple trashers like chapel or with reactions like traders or watchtower. One fun thing with reactions is to remember that you can do this on your turn. E.g. your opponent has 2 witches to your one but you've just played hamlet/witch and have 6 coin and a watchtower in hand. Top deck the gold, buy a curse & trash it.
3. Jump past them. Farming village, venture, adventurer, etc. can mitigate curse troubles by ensuring that most of the time the curses go straight from your deck to the discard. Hunting party and golem can be particularly effective here. Cards that let you play with top of your deck like spy, duchess, and cartographer all move curses from deck to discard with no trouble.
4. Discard for benefit. Vault is the big one ensuring that even the most curse laden hand is a gold. Cellar, secret chamber, young witch, inn, etc. can all make good use of discards and curses matter less.
5. Hide them. Island, native village, and haven all allow you to see curses less or even never again.
6. Play a top deck game control game. Here you let the curse into your discard and make sure that the cards you get in hand rarely have a curse attached. For instance, KC/KC/scheme/scheme/monument/monument sits on the top of your deck, buys a bunch of green and scores massive points each turn without ever worrying about the bottom half of the deck. Likewise some setups of royal seal, develop, and watchtower can leave you playing mostly off the top of the deck. A harder trick is inn abuse. Near the end of each shuffle, acquire an inn and pull all your actions out of the discard into your deck. With some setups (e.g. highway/IW) you can never draw a curse for 12 hands.
7. Embrace the bloat. Gardens is the big player here. Mitigate or overcome the penalty with lots of gardens & huge decks. As a bonus you only need to deplete gardens, curses, and estates to win. Philosopher's stone is another possible plan as big bloated curse decks = huge payout stones which can lead to double province turns fairly easily.
8. Reflect them. Ambassador & masquerade let you give the curses to your opponents & do something useful for you.
9. Prevent them - moat and lighthouse mean you can try to keep from receiving them in the first place. Having a deadish card in your hand like moat or lighthouse can be bad as their effects are not that great for the price of an action. On the other hand they can save you a lot more dead cards later and can be insanely effective in multiplayer games or multi-attack games.
10. Play the odds to win first. Take something simple like witch, treasure map, and pawn. Your opponents open witch/pawn and you have a 4/3. Your odds of winning are pretty lousy if you go for witch yourself, however going for treasure maps can allow you to have some odds of hitting 4 golds early and pushing out quick points/cash before the curses drown you. Remember the best move is whatever improves YOUR odds the most. Even if a curse giver is strictly better than some other combo; your odds of coming from behind in a mirror can be pretty low.
So feel free to mix & match, but I believe this every possible way of dealing with curses currently supported. There are many ways of beating the cursers; just use what you can when you can.