The biggest disadvantage is that there may be security and control concerns. Any servers you own are in someone else's datacenter. It is important to ensure that there is rigorous security access into this facility. However, because it is the primary business of this service provider, there will most likely be fairly extensive security access control. You also want to ensure the datacenter staff is experienced troubleshooters and quick to resolve connectivity and network performance problems. Finally, it is important to gauge the profitability of the co-location service provider you select. If this service provider goes out of business, it may be difficult to get your server out of the service provider datacenter. Understand how portable the data on the server is and ensure backups are readily available from another site, especially if this server is hosting production data.
Some companies that provide co-location services include ColoSpace and Colocation.com and amongst others. They all provide either strictly collocation services or co-location as part of their set of services. Since co-location is most advantageous when the service is within your location, it is best to perform a search on co-location and possibly your city or state.
Renting Infrastructure in the Clouds
Renting or leasing from a cloud infrastructure is a more recent concept and option that some organizations are utilizing where the infrastructure (servers, software, etc.) is effectively in the internet cloud. This service is sometimes known as cloud computing but have a variety of other names each with slightly different focuses and approaches including software as a service (SaaS) sometimes known as the application service provider (ASP) model, platform as a service (PaaS), application infrastructure provider (AIP). In this article we will call it "cloud infrastructure" where you have a hosting service provider that may provide hardware, tools, software, network, etc., that is available to subscribers. It follows a pay per use approach that may be seen as utility computing, since you are charged for the portion you are using.