1 Barracks Fast Expand is the most standard of terran builds right now. It's used almost every game in high level TvP, it's used somewhat often in TvT, and with the recent patch it might become standard in TvZ as well, since hellions will be less effective.
Because of how often it's used, a number of variations have popped up. Most of these are very similar and involve going for 3 barracks and 2 gas right after the command center, but there are small differences in timings from changing up various things in the build, and I'd love to see this discussed more in the comments, hence the [D].
For now though, the "guide" itself:
+ Show Spoiler [1 base] +
This is the part with the least amount of variation. The only trade-offs you make here are denial of scouting information, number of marines, and CC timing.
First, when you hit 9 supply, rally your CC to wherever you want to build your depot (at the wall for scouting denial, next to gas for economy) and make sure you have another SCV queued up. When the depot finishes, use that SCV to build a Barracks on 12 and scout when the Barracks is completed. Now for the variations:
Greedy 1 depot style
16 Orbital Command and Marine (you have enough minerals for both at once)
17 Command Center on low ground (since you can't deny scouting)
17 Supply Depot (complete wall-off if you started one)
This gets you a really early Command Center that should start building at around 3:05-3:15. The downside is that you don't have as many marines with this option early on.
2 Depot Polt Style
This isn't unique to Polt but I've seen him use it on stream and I've found it better in every way to the style following this.
16 Orbital, Marine, and Depot all start at once
17 Marine
Rally the depot-building SCV to your natural and build the CC when it gets there. Your natural should start at around 3:30, a bit later if you make an SCV when the orbital finishes.
FilterStarcraft Early Wall-Off
From http://www.youtube.com/filtersc. He's a masters player who gets from Bronze to Masters with 1 rax FE pretty much every game, and a partial inspiration for this guide.
14 Depot (rally at 13 supply)
With this, scouting workers will almost never get into your base. If you want your opponent to think you might possibly 1/1/1 you can build your CC on the high ground, but Filter's is always on the low ground.
16 Orbital Command and Marine
Constant Marine/SCV production off this will give you 400 minerals at 3:45 (but send an SCV down earlier) which is when you will build your CC. This build cuts the least amound of "stuff" but since your depot and rax finish at the same time, you can end up with workers on awkward sides of your wall.
+ Show Spoiler [2 base] +
This is where things get interesting. I'm mostly going to go over what FilterSC covered, which was close to the mid-April standard, and then go over what MVP did in his recent GSL match to improve on that. So yeah, spoilers are coming.
Former Standard Bio
Depot with first 100 minerals
Bunker with next 100 unless you see greedy play, then delay it
2 Barracks at next 300 minerals
2 Gas at next 150 minerals
Send 6 workers to your natural, 4 to gas geysers, and turn your natural into an orbital
Marine heavy: Wait for 125 gas and marine production cycle to finish, then build 2 reactors and a tech lab.
Marauders: Do the same but with 100 gas, 2 tech labs, 1 reactor.
At around 6:50, put down a factory.
At around 7:25, put down an ebay and start stim (combat shield for TvT). Get +1 attack when ebay finishes.
When the factory completes, build a starport. For pure bio, get a reactor on the factory and transfer it to the starport. For marine tank, get a tech lab on the factory and no addon on the starport for now.
With good macro this should come out to about 50 workers and 50 army supply at 10:00. Stim, +1, and medivacs should be ready, and siege mode should be on the way for marine/tank, or combat shield on the way for bio.
None of this is new, though, Filter covered it in his guide. I'll go over a few variations on this, then go over the weaknesses and some juicy MVP stuff.
Mini-Variation:
You can get the depot after the rax and gas, but you'll be stuck at 27/27 for a little while. It doesn't matter too much though.
Variation 1: Apollo's Bunker Paranoia
In Apollo's Terran tutorial, (http://www.youtube.com/dapollo) he says, "Get a second bunker (against Protoss), don't argue, just do it." A lot of Protoss will try to rush to a gateway all-in with possible immortals after seeing a 1 rax FE, and this is nearly impossible to hold with one bunker. Blindly getting a second bunker, and even a third if you don't see an expansion, can help deal with all-ins.
Against Zerg, bunkers are important, but you also need to wall-in to deal with potential roach/bane busts. On ladder players tend to play extremely reactively so you'll see a lot of all-ins against 1 rax FE. In the replay section you'll see 3 of my replays where I blindly get bunkers or wall-in and defend. I'm not very good but it does save me in each game. You won't see pros doing this much since every edge counts and most players have a gameplan from the start of the game.
Also, a turret at your expansion is nice TvP to keep out hovering observers.
Variation 2: fOrGG's TvT bio style
http://www.twitch.tv/ogsforgg/b/317685816
Skip to about the 7 hour mark to see what I'm talking about.
fOrGG goes for a 2 depot 1 rax FE (Polt-esque) but then goes for a TvT variation that's very outside the current norm. Most Terrans go for 2 gas before 2 extra rax (variation 3) but fOrGG's style looks a lot like MVP's TvP style for a while, except fOrGG's ebay is slightly earlier.
However, when the factory goes down, things become very different. fOrGG takes the 2 reactors as usually but gets double gas, doesn't get any marauders, and gets 2 factories with tech labs as well as a reactored starport at around 10 minutes instead of pushing, allowing him to go heavy marine/tank off 2 base and get a third.
Note that there's no early aggression from his opponent, but the high marine count and early e-bay allowed him to be relatively safe.
Variation 3: Double gas
I could only find one replay of this but I've seen it a lot. Most of the time getting the 2 gas before adding double barracks means that you can make a smaller push at around 9:30 with fewer M&M but with all your upgrades and medivacs, and that's not worth going into too much detail over since most things are the same. However, there's another option that lets you deal with cloaked banshees much easier than the fOrGG style.
After the double gas, don't add on double rax at all, but make a factory instead. Then make a tech lab on the factory, a starport a reactor on your barracks, get a third gas, and transfer your tech lab to the starport. Scan your opponent's base. If you see banshees, get a raven and a viking and you should be able to deal with it without an e-bay. Otherwise you can use banshees to harass before going into bio or mech, as you see fit. For bio, you should be able to add 2 ebays at around 9:00 and do a fast upgrade style.
The replay of this is ZenexSparta (fast expander) vs LastShadow (banshees into mech) in the replay section.
Weaknesses of all the above
You have very little map control and you don't have production when addons are building. Fortunately, MVP has addressed this.
MVP's goodness
http://www.gomtv.net/2012gsls2/vod/67130 (games 1, 3, 4)
This is a very recent series, watch out. However, I haven't seen anyone else do this exact thing.
Everything is normal up until you start mining gas.
Then the first 25 gas go towards a tech lab, leaving the other barracks naked and making marines.
Start stim as soon as possible, and push out with what marines aren't in the bunker to take the watch tower(s).
At around 6:25, add an ebay, a factory, and a 3rd gas. This allows timings to be much earlier without cutting into production. Only build marines from the tech lab barracks.
+1 when ebay finishes, reactor/starport when factory finishes.
Then get 2 reactors on your barracks at 7:50, but keep making marines from the tech lab rax.
When your starport finishes, start medivac production, get a 4th gas, and start marauder production. Your reactors should be finished as well.
Start combat shield. Your push should come at 9:30 and be almost as strong as the 10:00 push from the "former standard".
Note that you can also go for a more marauder heavy style like MVP did in game 4. Just get a tech lab and reactor at the same time instead of 2 reactors in that case.
+ Show Spoiler [3 base?] +
This is the part of the guide I'm least sure about, and I'd like input from comments.
Standard 3rd base transition
After the push (make sure to lose as little as possible, you usually won't win with a 10 min push so don't force it) get +1 armor and 2 more barracks. (use whatever addons counter his units, which is usually reactors unless you're facing heavy colossus/storm play)
Then make a 3rd command center on high ground if you have no map control, on low ground if you have some.
Get a second ebay and an armory when +1 armor is halfway done. This will allow you to start 2/2 at a reasonable time. 3 base marine heavy 2/2 pushes are strong in all matchups, watch some of Heart's longer games to see what I mean. Get concussive shell because why not.
Finally, go up to 5 or 6 gas and add whatever production you want. 9 barracks, 1 factory, 1 starport is good for marine heavy or MMM, 7 barracks/2 factory/1 starport seems standard for marine/tank but I'm less sure of that.
You'll want a second reactored starport against colossi and a ghost academy/more tech labs for playing against storm/upgrades/archons.
2 base all-in variant
For reference, see MVP vs Parting game 1 and Jjakji vs JYP game 1.
MVP's version:
Add 2 more barracks and do not make an armory, you will be pushing with +1/+1. After getting 4 medivacs, get 8 vikings if you're facing colossus. (this is all off 1 starport, so you can't miss production rounds) Vs anything else get more medivacs. The attack should come at around 13:00, MVP pulls SCVs but it shouldn't be required.
Jjakji's version:
Do the same but get +2/+2 and +1 ship weapons (vs Colossi). This delays the push until 15:00 but makes it much stronger.
I'll update this section when I see this done more often. The one common theme seems to be that you don't have the resources or time to get ghosts.
Replays:
http://www.gomtv.net/2012gsls2/vod/67163 Jjakji vs JYP 2 base all-in.
http://www.gomtv.net/2012gsls2/vod/67130 MVP's games
http://www.twitch.tv/ogsforgg/b/317685816 fOrGG's games (7 hours in)
http://drop.sc/176237 ZenexSparta's safe double gas
My own (low level) replays:
http://drop.sc/176238 TvZ Marine/Tank with bunker harass
http://drop.sc/176239 TvP vs 4 gate
http://drop.sc/176240 TvZ Marine/Tank with no harass