Being a new member and player myself, I like the Ruy Lopez for white, and the Pirc for black. You can find both openings on the site here.
Good beginner openings?
As a beginner, I've chosen to go with the Italian opening (1.e4 e5-2.Nf3 Nc6- 3.Bc4).
If my opponent plays 3...bc5, I can go with the Evans gambit (4.b4). I haven't tried to learn many lines, I've watched some videos and read some simple material on it, to get the general idea of the opening (attacking the f7 square, trying to prevent Black from castling by forcing him to move or by destroying his kingside pawn structure through a sacrifice). I've remembered some lines from the vids I've seen, some of the games I've played with it have given me some interesting feedback, and I try to play a master game in which it's used every other day.
If my opponent plays 3...Nf6 (two knights defense), I play 4.Ng5, aiming for the Lolli attack. Same idea, I don't try to remember lines by heart, but rather the main idea behind the opening. I've watched vids, I play a master game where it('s used every other day.
If my opponent plays something else, I just try to develop my piece while taking into account what he's doing.
I like it so far. The Italian game seems very natural to me, so I feel that playing lines that start from there makes sense. The way I learn them gives me time to focus on my ongoing games, chess mentor, and reading/watching more general material. I think I'm learning faster than if I was trying to learn the lines by heart, as this does not appeal to me at all, and with my way the few things I learn are learnt once and for all, as I understand the reason behind the good move/bad move.
Just a beginner's 2 cents..

Being a new member and player myself, I like the Ruy Lopez for white, and the Pirc for black. You can find both openings on the site here.
I originally did enjoy playing the Ruy Lopez, but after speaking to other players on this site, they seemed to agree that a Ruy Lopez was not a particularly good opening for a beginner?

As a beginner, I've chosen to go with the Italian opening (1.e4 e5-2.Nf3 Nc6- 3.Bc4).
If my opponent plays 3...bc5, I can go with the Evans gambit (4.b4). I haven't tried to learn many lines, I've watched some videos and read some simple material on it, to get the general idea of the opening (attacking the f7 square, trying to prevent Black from castling by forcing him to move or by destroying his kingside pawn structure through a sacrifice). I've remembered some lines from the vids I've seen, some of the games I've played with it have given me some interesting feedback, and I try to play a master game in which it's used every other day.
If my opponent plays 3...Nf6 (two knights defense), I play 4.Ng5, aiming for the Lolli attack. Same idea, I don't try to remember lines by heart, but rather the main idea behind the opening. I've watched vids, I play a master game where it('s used every other day.
If my opponent plays something else, I just try to develop my piece while taking into account what he's doing.
I like it so far. The Italian game seems very natural to me, so I feel that playing lines that start from there makes sense. The way I learn them gives me time to focus on my ongoing games, chess mentor, and reading/watching more general material. I think I'm learning faster than if I was trying to learn the lines by heart, as this does not appeal to me at all, and with my way the few things I learn are learnt once and for all, as I understand the reason behind the good move/bad move.
Just a beginner's 2 cents..
Thanks for the feedback, Italian game definitely appears to be a natural opening, and one in which I can easily develop my pieces. That was one of the problems I found with the Ruy Lopez, I often found it hard to develop.

I find it interesting that all the responses have been from beginners. You should be getting advice from stronger players who know better, not from other beginners. Not that the beginners are necessarily wrong in their choices, but if you can learn from the mistakes of people who have been there and improved beyond beginner level by learning from their own mistakes, then it's a good idea to do so.
That said, there are a LOT of strong players and professional chess coaches who say that beginners should stick to playing open games, and as an intermediate player, I agree with them. Those are usually openings starting with 1. e4 e5 in which a pair of pawns near the center are exchanged early.
Bguigz's recommendation of the Italian (1. e4 e5 2. Nf3 Nc6 3. Bc4) is among the most popular openings for this, though you may want to stick with the easier main line Giuoco Piano (4. c3 and 5. d4 against 3. ... Bc5) instead of the Evans Gambit.
In response to Hicut, the Ruy Lopez is a great opening for strong players, but it doesn't necessarily lead to the type of open centers and relatively straightforward tactical play that beginners need to learn from, which is why it's generally recommended for beginners to avoid it. The Italian has that bishop on c5 aiming at black's weak f7 pawn, which can lead to some fun tactics.
Striving for open, tactical positions also means answering 1. e4 with e5 as black. Again, stuff like the Pirc, French, Sicilian, Caro Kann, etc are great openings for stronger players, but you should learn to handle open, tactical games first, then worry about the fancy positional maneuvering later.
And this is somewhat of an unorthodox suggestion, but I found that answering 1. d4 with e5 (the Englund Gambit) is also good for getting an open position as a beginner. You'll lose a pawn immediately, but it'll lead to an open, tactical game, so the player who calculates the tactics better will always win, regardless of white having an extra pawn on the second move. After the obvious 1. d4 e5 2. dxe5 Nc6 3. Nf3, black has a couple of main lines to choose from, including 3. ... Qe7 (often followed by Qb4+) and 3. ... f6 4. exf6 Nxf6.
The down side of the Englund Gambit is that it really is unsound, so you'll have to learn a new opening to replace it with once you hit intermediate level (maybe 1600-1800 rating).
In my opinion the opening isnt such an important point for a beginner. Just make use of the 3 golden opening rules:
1. pawn in the centre
2. Play your Knights (preferably not to the a of h-line) and Bishops
3. Secure your King (mostly 0-0 or 0-0-0)
When you do this you will lose very occasinally and play some nice games. In the beginning you have to improve your middle game, this is much funnier then studying some openings. Also in these opening you have studied there are some lines you dont know. If your opponent plays these you can lose very fast by an opening trick. This is much more unpleasant then losing in an opening if you didnt spent hours studying.

It bears pointing out that playing people near your rating as a beginner means they won't typically know any more opening theory than you do. I'd be shocked to see a 1200 rattle off 12 moves in the mainline Ruy Lopez and not be using an opening database to do so.
I'd say play what makes sense to you, however I agree with Fromper that learning an open game is going to give you a lot more mileage in chess understanding than trying to play super positional games at the moment.
There are number of players with a rating like 1200 who play 12 lines in the mainline of the Ruy Lopez, but when you play a move that's theory (and is not a standard blunder) they dont know what to do anymore. If you understand what you are doing the opening is not so important till a level of 2200-2300. There are even IM's who have a little opening knowledge.
Against lower rated players or players with much opening knowledge I play sometime moves like 1. Na6, of course this isnt the best opening, but it is playable. But more important is that your opponent has to play chess and not show their knowledge of an opening.
Here's the rationale behind my decision to try and play the Evans gambit:
1- I've read several times that the Evans gambit tends to bring "wild" middle games full of tactics opportunity, while the Giuocco Piano tends to lead to more positional games. I think at my level (beginner), losing an interesting game in which there has been a lot of tactics involved will teach me more than winning a slow-paced positional one, as I just don't have the experince or board vision to appreciate the positional advantages or imbalances..
2- As a beginer, when I'm not sure about what to do, I tend to either to a useless move or a big blunder. The way I understand the Evans, you gain a slight development advantage in exchange for a pawn. As White has the initaitaive, this advantage remains as long long as White keeps Black on his toes by throwing threats at him. The moment White loses a tempo by playing a move that's not a threat or a reinforcement of the attacking pieces, Black get the oppoprtunity to build a solid defense or develop his pieces in a way that makes White's development advantage disappear.
So the Evans forces me to play each move with a real intention behind it, as I know I can't afford to play waiting moves. It's made easier as I try to follow the general idea behind the opening instead of specific lines.
The reason I chose the Italian game was also because if I find out that the Evans os too much for me or if I end up not liking it, I can always go back to the Giuocco Piano, so I won't be totally lost..
Dunno if that makes sense, but after thinking about it a long time, it sounded like the most logical option. And once again, as those opening (Evans, Lolli attack, Giuocco Piano) seems rather logical to me, I can get better at them bit by bit without investing too much time on opening study (more time for more general study like tactics or endgames).

bguigz I agree with your decision to play the Evan's over the Giuco. Not only do I think that it is better from an improvement standpoint, but it is also practically a much more dangerous weapon.
What are the good openings which a beginner like myself could learn and use?