There are already some very good comments on this thread but I thought I would add a few based on my own experience of nearly three decades working with startups in Silicon Valley.
If you have a truly great name, and you are at an early stage, you can easily have the name poached. Since a trademark registration can prevent that risk, it can be helpful.
Under U.S. law, whenever you use a mark in commerce, you accrue common-law rights coterminus with the scope of that usage - meaning, first in time gets superior rights to others for the geographical area of first usage. However, for any mark regarded as important, it is normally inadequate to rely on common law rights and it is therefore usually much stronger to register the mark to ensure solid protection throughout the relevant domain in which you seek protection (usually, a federal trademark registration).
With a federal registration, you can do either an in-use application or an intent-to-use (ITU) application. Most early-stage startups go with ITU. In-use requires that you already have used the mark in interstate commerce. ITU imposes no such requirement. It is comparatively simple to do an ITU application and not too expensive to get the application on file and there are few technical complexities associated with it (for example, you don't need to submit specimens at the time of application). With an ITU application, you go through a 12-to-18 month process by which the USPTO determines whether the mark is registrable and whether it is available for the class of goods or services desired. If it is, and is approved, you get superior rights over all others to use the mark for that class of goods of services dating back to the date of the original application (you do have to file a Statement of Use at some point demonstrating actual use in interstate commerce but you can normally take your time about this).
As far as practical examples of the swiping problem, the founders of what is now Autodesk lost their first choice of company name years back after casually presenting it to others but not registering it. I have also had unscrupulous types try to do this with good names proposed to be used by some of our client companies (in one case, we did an ITU application that beat the poacher by a day, the poacher being a competitor who was just out to cause trouble).
Just as the ITU procedure makes it easy to register a mark without having ever used it, it also makes it very easy for someone to poach that mark at any time if it has never been registered. Therefore, until you do a registration, there is always a theoretical risk that this might happen.
To sum up:
Can an unregistered mark used by an early-stage startup be poached? Most definitely. Does it happen in practice? Very rarely. Against that context, it is up to each founding team to make a cost-benefit assessment of whether it is worth front-loading the legal expense (usually about $2K to $3K for a federal registration) to guard against that risk. The usual answer is no. But, for any really valuable name, it should be yes. From my experience, in practical terms across a range of early-stage startups, it can easily be said, however, that 90+% do not bother with such registration at the start on cost-benefit grounds.
Edit: By the way, if you do go to the trouble and expense of registering, make sure the mark is likely registrable, meaning (in most cases) that is not purely descriptive of what your product or service does (this is the most common problem by which founders get frustrated, and run up a lot of expense, in early-stage trademarking).