Which opening should I play against e4

personally I usually play the french, e6. But it comes down to preference  Pick an opening, study it and understand it  Get lots of experience playing it.

No matter what opening you pick you will eventually probably run out of the moves you memorised. How well you do then depends upon how well you understand the position you are in.

If you don't know what to do then you should continue playing e5, it usually goes to pretty standard Italian game/ruy Lopez positions when I play it. The only two other responses you should probably familiarize yourself with are the king's gambit and scotch. I feel like that sums up pretty much everything I usually see after e5.

If you are playing me, then after my 1. e4 you should play 1. ... g5, followed by 2. ... f6

I agree with Neil. If you're unsure, play e5. Anyway, lacking ideas isn't a good reason to stop playing an opening, it's a good reason to learn more about chess and those positions specifically.

Pirc.  As white you are surely facing kingside fianchetto defenses, might as well learn them, beginning with the Pirc or Modern against e4. 

For the sake of consistency, you can go 1....Nf6 against e4 as well. The Alekhine is a respectable opening.

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My personal favorite opening against e4 is Italian Game, Two Knights Defense:

You can use many openings, but I would suggest the Sicilian. It often scares club players and I just love it.

Is that modest and polite? Go ethical!

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The Cara-Kann was first mentioned in 1590. It took until 1880 for the Viennese M. Kann player to show it H. Caro the Berlin player. The defense reached its peak popularity in the 1920's when Capablanca, Nimzowitsch and Tartakover all played it. The defense also found favour with Botvinnik. It is similar to the French challenging white's command of the centre with 2. ... d5 but has the advantage of allowing black to develop his queen's bishop.
As in the Sicilian black hopes to create an imbalance in the centre and thus avoid the drawing possibilities which are implicit in symmetrical positions.
The opening can be played very solid with 0-0 or at times lively with .. Nf6-d5 ... Bd6 ... Qc7 and ... 0-0-0 changing a general queen side attack plan into a counter king side attack.

I used to hate the French, but now I love it, especially the advanced variation, as both black and white.  It's just complex and beautiful. I also play the Sicilian quite a bit. I don't like to play the Dragon as black, simply because if white knows what they are doing then they can launch a pretty powerful kingside attack.  In the Sicilian I play either Franco-Sicilian, Najdorf, or Scheveningen variations. 

I started reading up on Alekhin's Defense just for fun, but I don't reccommend that opening for beginners since it's really complicated and extremely risky. 

I stopped playing e5 in response to e4 because I am a positional player more than a tactical one, I've found out in the past few months.  I was fed up with playing the four knights game at every single OTB I went to.

I don't have a lot of experience with the Caro-Kann or Scandinavian systems as black, although I play against them all the time as white.

if you're beginner play e5 against e4. It is important to learn these positions. If you're not beginner play e5. it is important to understand these positions.

I'm starting to like the Caro-Kann as Black, playing the variations where I get my Q-Bishop out to f5 or g4 before playing ...e6. That way, even when White grabs a lot of early spaced, I don't have a cramped game and White often gets his pawns in bad positions or offers me a great N outpost on d5.

Whatever Opening you decide to pursue, find a book that explains goals of the openings. Very often you're going to be out of the book very early. Play some live and/or against a chess engine games, save the pgn files and analyze them - which will help you remember the games and what to do next time.

For example, in the Caro-Kann, 1 e4 c6 2 d4 4 d5 3 e5 Bf5 is in all the Caro-Kann books as the preferred Black 3rd move in the Advance Variation. But, while 4 c4!? is often listed with "!?" in the books - they seldom goes any farther.  In fact, it's only a footnote in MCO and NCO and occupies about one sentence in FCO.  The "book" reply, where you can find one, is 4...e6.  I played 4...e6 in a 10-minute game I played here (which I lost in an equal position by not paying attention to time!) which continued 5 c5: 

Houdini (Chess King) and Stockfish (Lucas Chess) engines find that to be a good move - but you won't find it in: Soltis's A Black Repertoire for the Rest of Your Chess Career, Schandorff's The Caro-Kann, Lakdawala's The Caro-Kann Move by Move, Gallagher's The Caro-Kann (Starting Out), Suetin's Caro-Kann Defense, Houska's Play the Caro-Kann, Davies' and Martin's The Caro-Kann Defense, or Watson's The Chess Openings, V1.  I don't own all those books, but had the opportunity to check them out from a friend with a huge collection.  The point is that the books are only going to take you so far and you're better off looking at tactics: good opening play is only going to get you to a playable middle game.

The chess engines liked my reply, 5...b6!, but didn't like 6 b4? bxc5? - preferring 6...a5, which I'll remember.

Most of them didn't give a significant advantage to either side with the preferred or ? moves, so I did a database search:

Using Chess King's "Search" of its "Gigaking" database I found 13 games through 5...b6! where Black won 9, drew 1, lost 3 (a search of pgnmentor's CaroKannAdv free database found 2 games, both of which Black won, the free Kingbase B00-B19 found no games).

12 of the 13 Gigaking games continued 6 b4 (Black won 9, drew 1, lost 2), 9 continued 6...a5 (Black won 6, drew 1, lost 2) and, instead, one continued a my game, 6...bxc5 (Black won).

So, I learned something about the opening by playing the game then analyzing the game and looking at how others handled the game. I'll play the same in the future against the early c4 and c5 moves, striking them with b6 and a5 as recommended.

Playing through those 13 games, Black succeeded primarily by Queenside attacks.  So I'm a little better prepared the next time my opponent tries to cramp my position in the Caro-Kann

Correction to my diagram: I shouldn't have shown the 6 b4 b6  moves shown in the diagram - they weren't played at that point in the discussion.