From a very legalistic reading of the rules, you can use assassinate only once per encounter. Using it requires the opponents be surprised; they are only unaware of their opponents once in a fight; and stealth doesn't grant surprise status.

In effect, think of it like this: a surprised opponent is one that is entirely unprepared for being in a fight right this instant. When you attack an unsurprised opponent from hiding, they are already expecting attacks, so they are less vulnerable then when surprised but more vulnerable than when they can see you specifically.

It might actually be more and less complicated than that

However, that is a fairly conservative legalistic reading. It requires reading the description of surprise as ungenerously as possible—which, in general, is the safest way to read a rule when you're a player. Better to be right that you don't get goodies, than expect goodies and be wrong, yes?

That said, D&D Next is going to be weird for any player from the last decade and a half of D&D editions, because it has the explicit goal of reclaiming the heritage of AD&D and earlier editions that 3e left behind. And a major part of that heritage (for good or ill) is those editions' interpretability. Unlike 4e and (mostly) 3.x, the rules were only hard-and-fast where the rules were unambiguous, and where they were ambiguous the DM was expected to decide what worked best for their home game. When something was unclear in the rules, sometimes there was an official answer, but as often there wasn't.

This was considered a feature by the designers, especially in the original edition of D&D and in the Basic line. This was slightly less the case in AD&D because it was also meant to be the "tournament edition" of the game, but it never shook that heritage and it has interpretability very deeply ingrained into its structure and how the rules are explained.

Arguably, 3e didn't shake that heritage completely either. 3.5e got closer, but still has a few lacunae that drive people to distraction. 4e was the attempt to refine it to perfection and eliminate even the possibility of lacunae... and WotC didn't like the customer rebellion that edition caused. Hence Next, and why it is going "backwards" in many ways.

It's debatable whether Next is going "backwards" in regards to interpretability specifically, but as I hope I've shown, it's a distinct possibility that the rules for surprise and stealth are every-so-slightly unclear on purpose.

So what?

Well, so what? If the rules are unclear, then making the most conservative, power-limiting interpretation is correct, right?

Power problems might not actually be problems

Well, no, not exactly. Next is designed to have a much flatter power curve than any prior edition from Wizards of the Coast. A neat thing about a flattened power curve is that it makes the "sweet spot" of most-enjoyable levels much wider, which is a large part of why they wanted it. But also, as anyone can tell you who has experience with non-WotC D&D editions, a very flat power curve also means that character power is less variable and, often, a more-powerful character doesn't have the ability to travel far enough "upslope" on the power curve from the rest of the group; if the power curve is flat enough, or the character's advantage is unoptimal enough, they simply don't cross the threshold of problematic power difference.

So that's a neat feature. It was taken for granted by AD&D DMs and players, and it gave those groups much more flexibility and power to create interesting adventures and mixes of PCs without running into balance problems or putting constraints on story and adventure design. It was only in the 3e era that "power disparity" entered the lexicon of D&D players.

With Next's flatter power curve, it's entirely possible that power disparity problems are only in our habits learned from 3/4e, and aren't applicable to Next.

Surprise and stealth

So if Next doesn't have the kind of power-imbalance problems that we're used to having to squash, our habit of reading the rules as conservatively as possible may not apply. It wasn't necessary in pre-3e D&Ds, and maybe it won't be necessary with Next.

And if interpretability is a deliberate design feature of Next, then there may actually not be an official answer.

Combine these two possibilities, and you have an interesting result: it might not matter which way you read this rule. And if it might not matter, then different DMs might run this differently in their games, with some allowing Stealth to be used to hide your presence, and that counting for triggering "presence" condition necessary for surprise and assassination criticals.

This is often how AD&D DMs ran thieves' backstab ability. Given how much Next is attempting to recapitulate AD&D and earlier editions, and given how these rules around surprise and stealth look suspiciously similar to those earlier editions' rules for surprise and stealth, and given how the power curve of Next has been brought back into line with the power curves of AD&D and BD&D... I would not be surprised at all if the answer to this question was: Ask your DM.

Yes...sort of. More at L1 than at other levels though.

For a brief look at this, let's look at the 4 basic L1 characters and see what their defined combat options are.

• Wizard: 3 L1 spells/day (they get the extra from an afternoon nap). 3-4 cantrips. Generally the wizard has the most combat options. They have more daily spells than the cleric and they have several offensive cantrips to choose from (firebolt and ray of frost are the two that come to mind, they have another). Their cantrips either do a good bit of damage or slow or push. This gives them good options in melee, at range and on the daily power front. Lots of options on their turn.

• Cleric: 2 L1 spells/day, 3-4 cantrips. The cleric only has 1 attack cantrip, but the current cleric is designed to be played by a dwarf, and they get a genuine melee option (with proper stat allocation, it's better than their cantrips at L1). This gives them a good number of options (several of their cantrips are cool utilities in combat too). So they have a good number of choices on their turn.

• Rogue: no spells, all powers phrased in the form of Melee Basic Attack, and their cool movement power doesn't kick in until L2. The L1 rogue's only way to reliably generate Sneak Attack is to actually get into melee and find a buddy to stand next to their target (The other way is to stay at range, and also find a buddy to stand next to their target). Otherwise the L1 rogue does spend half their turns hiding (which is sad). So yeah, limited options here in combat (L1 rogue out of combat is a skill monkey and that's cool). Most of the combat decision for the rogue are whether or not to eat an opportunity attack to go over to the fighter's target to deal Sneak Attack on it.

• Fighter: Even more boring than the rogue. He has two main choices: which target am I going to hit with my weapon, and is it time to burn my Second Wind. Granted, this makes the fighter the most self sufficient character, but it doesn't provide many interesting combat options. Similar to the rogue, the fighter's best option sometimes is to eat the Opportunity Attack and walk over to the rogue's target so he doesn't have to eat the OA himself.

So yeah, L1 is pretty boring for the Fighter and the Rogue. Here's the good news: L1 is designed to be very short. And L2 is where a ton of the good stuff is for the Fighter and the Rogue*. The Rogue gets their class defining power: Cunning Action. This lets them hide, move and attack all in one turn (or disengage, move and attack all in one). This is the power that makes the rogue tick in a lot of ways. For the Fighter, they get the power that lets them compete with the rogue in damage 1-20. Their Action Surge power gives them a second meaningful per rest choice in encounters: they get another action on their turn.

Neither of these choices really solves the "I attack the goblin with my sword until he's dead." However, in many ways, this isn't all that different from the level of choice an Essentials class character has on their turn in 4e (well, it's fewer options, but it's fairly close by L2 I think).

Ultimately, breaking the "I attack the goblin until he's dead" cycle is not something that 5e addresses very well. It's left to the players to "try something interesting" to get the upper hand, and this seems to be encouraged by the system. Like it or not, this is 5e's design paradigm for Basic D&D. With the PHB coming out next month, two new martial archetypes for the fighter, and two new sub classes for the rogue should provide them with additional options on their turn (Eldritch knight is a gish type with spells, and the Battle Master fighter uses combat expertise dice to do other stuff).

*I think there is a pretty good reason for this. I believe this is largely to limit the effectiveness of single level MC dips into fighter and rogue to get some of their strongest powers (they already get a lot at L1, the fighter alone gets a fighting style, weapon and armor profs, and Second Wind.).