I can't come up with a better name for this model, but, not to worry, you'll recognize it right away. In this period of renewed discussion of "how to make money," I'm trotting out my favorite -- perhaps the best one for a startup today.
Let's take the explanation in two parts. Pseudo-Business Software is software used to conduct business, but which is not necessarily sold directly to businesses. Put another way, it is priced and and offered in such a way that individuals and small work groups inside of businesses can buy and use the software directly, without larger purchasing approval and without IT department approval. It offers a businesslike function so that it is easy to justify on an individual expense report -- and it's cheap enough that some folks may happily pay for it themselves just to be more effective at work, the same way they might shell out $25 for a DayRunner or $50 for a nice portfolio without thinking twice.
YouSendIt fits this model: it offers an oft-needed business function -- transferring large files. It lets employees bypass the tortuous and unwinnable debates with IT over why and whether attachments fail, how to share files with others, etc. Pay a few bucks and if you can get to the web at work, you're good to go. Easy to expense or even pay for on your own. It's enterprise software sold cheaply and one user at a time.
JotSpot (now Google Sites) -- in its original freemium wiki form -- fits as well. Easy to justify as project groups scale and each monthly increment is a small charge. Instantly bypass all the broken collaboration infrastructure your company can't get right.
At the same time, these products are Pseudo-Freemium software. If freemium is software that offers one level of functionality or resources for free, with more available for a price, then pseudo-freemium is like freemium except that the free version is not terrifically usable as a business solution except to make the customer comfortable with the product.
YouSendIt has, and JotSpot had, free versions. Unlike many consumer freemium use cases where many users happily use the free version and never need to upgrade, these pseudo-freemium products are were specified so as to be more like a mini-free-trial.
IIRC, the JotSpot free account was limited to 5 users and 20 wiki pages, while YouSendIt free limits the file size to just shy of what I always seemed to need. There are countless other examples, ranging from single-user hosted source code services to online storage that offers only minimal free space.
The free version gives you the "warm fuzzy" of a free never-goes-away account and lets you see that the product works as advertised and won't embarrass you with some crazy or unprofessional aspect when you're asking your boss to sign for it on your expense report. These have always been the easiest-sell, no-brainer for-pay services that I've subscribed to. In general, they appeal to that certain purchasing area in people's minds -- next to the planners, a beer in the airport restaurant, or a nice tie -- as modest costs of being a professional that are either expensable or should just be paid for oneself.