This is not to be considered an exhaustive answer, but just a few points on the topic.
Since the question is also tagged with the [sql] tag, let me say that, in general, relational databases aren’t particularly suitable for storing data using the EAV model. You can still design an EAV model in SQL, but you will have to sacrifice many advantages that a relational database would give. Not only you won’t be able to enforce referential integrity, use SQL data types for values and enforce mandatory attributes, but even the very basic queries can become difficult to write. In fact, to overcome this limitation, several EAV solutions rely on data duplication, instead of joining with related tables, which as you can imagine, has plenty of drawbacks.
If you really require a schemaless design, “allowing an unlimited number of attributes”, your best bet is probably to use a NoSQL solution. Even though the weaknesses of EAV relative to relational databases also apply to NoSQL alternatives, you will be offered additional features that are difficult to achieve with conventional SQL databases. For example, usually NoSQL datastores can be scaled much easier than relational databases, simply because they were designed to solve some sort of scalability problem, and they intentionally dropped features that make scaling difficult.
Many cloud computing platforms (such as those offered by Amazon, Google and Microsoft) are featuring datastores based on the EAV model, where an arbitrary number of attributes can be associated with a given entity. If you are considering deploying your application to the cloud, you may consider this both as a business advantage, as well as a technical one, because the strong competition between the big vendors is pushing the value-to-cost ratios to very high levels, by continually pushing up on the features and pushing down the financial and implementation costs.