Since the new update some monsters open doors now, so a house is not safe anymore. Is there anything I can do to make my house safe again???

Wall up the door so they can't get in? One dirt block or two beside the door is usually enough.

Uhm, they have been able to do that since 1.2 for me.

There's a new a tall gate or something, perhaps that might block them completely.

I looked into the Terraria wiki and it seems that only a few monsters are able to open doors. I created a new world and there were no door opening monsters. Seems as if I have started near the crimson land.

Only during Blood Moons and certain other events, as far as I've ever seen. In the updated version, apparently, certain monsters can do it at any time. Putting furniture (any placeable item, really) in front of the door also barricades them effectively.

Aside from the above, though...build your house in the sky? Leave a ditch outside the door that monsters either won't walk into or can't jump out of? Use player-activated switches, wire, and active blocks to make "secret doors" that only player characters can use? There are probably more options, those are just off the top of my head.

Surround your base with lava.

Sure it will kill all of the other NPCs but fuck em! They overcharge you for stuff anyway!

Incidentally that does work without killing your friends. To be a room it needs to have a door but not necessarily a door going outside. I build all my apartments onto one large room (their doors opening into that one room) and seal in the whole thing in stone/rock. When I want to get in I use the Mirror. When I want to leave I either make a hole or keep a trap door on the roof ready. Eyes can get in there but zombies can't climb and even if they tried they'd get smoked in the lava moat.

On my larger playthrough during 1.1.1 I had a tree house in the air and it was very efficient but with switches and wires it sounds even better. Add Lava under or aound it as well like tinyE suggested with a 3x20 some tunnel directly under it so if they drop items you can swoop under and collect once in a while.

That reminds me, I still have to build a house in new my game.

I still haven't even tried 1.3.x yet, as I'm waiting for all the updates to settle down. I don't really want to be downloading and installing slightly altered versions of the full installer (or hotfixes) every day or two. It's cool, though, as I've barely even scratched the surface of the content in 1.2.4.1. : )

That's why I use Galaxy, much more convenient. I also disabled auto-updating so I can read the changelogs first. :)

Yeah, if you buy a lot of newer games -- as in, "within a year of the original release" -- or simply have a bunch of games (100+) in your library, a client like Galaxy would be a big help in that regard (doubly so once the rollback feature is implemented). But I have just over forty games on GOG (and that's counting all the permanently free ones, the promo giveaways, and a couple of Insomnia "critical hit" freebies -- several of which I'll likely never play unless I'm without Internet or cable access for a long period and I'm extremely bored), and I believe Terraria's the only one still being actively developed. I doubt I'd benefit much from using Galaxy, especially since I've never had any problem with the browser-downloaded installer method.
I might give Galaxy a try once it's out of beta, but I doubt I'll ever be a client-only gamer, as long as there's an option to not use one. =)

Well during events like the blood moon or a goblin invasion stay as far away from your base, the mobs always spawn where you are or they did anyway. So if your away from your base your pretty safe on that front, just in a goblin invasion pay attention to where the game is telling you they are coming from as they always start from the furthest point in your world in that direction and "advance" so meet them half way from your base. So if they are coming from the east head east as far as you can till you run into them, obviously the same if they are coming from the west.

Once you rescue the tinkerer from the dungeon you can start building traps, basic ones at first like say building a moat around your base and filling it with lava as well as placing some dart traps near by for those who might avoid getting killed by the lava and then covering it with active blocks(blocks that are wired up to a plate or switch) and then attach them to a switch or a plate if you want the trap triggered by the enemy stepping onto it. Personally I go with the switch method for that since once they fall in I can reactivate the blocks to prevent them from escaping their burning fate.

Later you can build more elaborate traps with fire, spears that drop onto their heads set to a 1 second timer and other crazy stuff. Trap building is a useful skill to learn post-hardmode when invasions and blood moons start getting nastier as well as the new event hardmode brings the solar eclipse, plus it can also help make doing the Pumpkin and Frost moon events a bit easier same with the frost legion(those are summonable only invasion events).

Generally not that great an idea when you enter Hardmode, as Wyverns love to spawn above a certain height regardless of your NPCs and their health. A lone Wyvern can easily tear up all your NPCs if you don't kill it fast.

Though you do also want to be careful about ground dwellings due to Wraiths, as they ignore walls (but can't fly).

You should also be careful about placing your houses near the starting spawn (use a bed to set another spawn) due to invasions. Most invasions have enemies that can bypass walls in some way and they ignore the standard NPC mob spawn suppression.

You can use Actuators (buy from the Mechanic), switches and wiring to set up some "wall-doors" like I've done with this house: http://imgur.com/zkcPREW

I added the doors to ensure that the rooms would still count as housing when the wall-doors were triggered. The teleporter is linked to one at the natural spawn point for easy access in case of an invasion.

Well yeah, but zombies and such can just hammer doors down, whereas protecting the entrance with a simple terrain block keeps them from getting into melee range. At least that's what I do early game and it works fine for me, but then again I don't really like Terraria and I've not gone very far in it.

the doors should have 'power' in this game. To make an iron door and discover it didn't change a thing from woods sucks.