It's pretty common for a complex app to make multiple connections to SQL Server. And, on SQL Server 2000 and earlier releases, it's also very easy for those types of app to cause perf problems by distributing their workload across their connections unevenly. To understand why this is, let's explore what happens when connecting to SQL Server.
When a client connects to SQL Server, it is assigned to a UMS scheduler using a simple round robin algorithm. The scheduler with the fewest users gets the new one. Generally speaking, a scheduler is simply a logical representation of a CPU. Although schedulers are not affinitized to specific CPUs and although the server can create more schedulers than there are physical CPUs in the machine, there is a loose correlation between UMS schedulers and CPUs. For each CPU on the system to which SQL Server has access, it will create a UMS scheduler to carry out client work requests (e.g., T-SQL language events, RPCs, etc.)
Each client is assigned to a UMS scheduler when it connects to SQL Server and never changes schedulers thereafter. This second point is important. Regardless of what's happening elsewhere on the server, a connection never changes schedulers.
Even though UMS schedulers are not hard affinitized to specific CPUs, because of the way that Windows schedules threads, a soft affinity generally occurs wherein a given UMS scheduler ends up always running on the same physical CPU. Although Windows can and will move UMS schedulers around as it pleases, a given UMS scheduler usually stays with a given physical CPU for extended periods of time.
So, let's say you have an app that opens four connections into SQL Server, and let's say SQL Server has four CPUs available to it. For the sake of simplicity, let's say your app makes all four connections at startup. Provided the current connections into the server are already evenly distributed across its UMS schedulers when your app connects, each of the app's four connections will be assigned to a different UMS scheduler. This will spread the potential work load evenly across the CPUs available to the server.
Now, what happens if those four connections submit workloads to the server that vary widely in size and resource requirements from one another? What happens if the first two connections actually do all the work, while connections three and four are barely used? Obviously, whole CPUs go virtually unused. Compound this with multiple instances of your app, and you can quickly run into contention for CPU (and even memory) resources on two CPUs, while the other two sit around idle most of the time. Because UMS assigns a client to a scheduler when it first connects and because each UMS scheduler winds up more or less soft affinitized to a given CPU, it's quite easy to get into a situation where a workload imbalance causes perf issues. The problem is so acute in some cases that I've even heard of apps using undocumented commands to determine what scheduler they end up on after connecting and intentionally disconnecting/reconnecting until they get the scheduler-connection alignment they think best. I don't recommend this, however. There is, fortunately, a much better solution.
The ideal solution is also the most obvious one: if an app opens multiple connections into SQL Server, attempt to spread its workload evenly across those connections. Then you don't care which scheduler or CPU you end up on because it really doesn't matter. And keep in mind that with the advent of MARS (Multiple Active Result Sets) in SQL Server 2005, you may be able to get away from opening multiple connections from a single app altogether.