There are two types of load testing - bottleneck identification and throughput. The question leads me to believe this is about bottlenecks, so number of users is a something of a red herring, instead the goal being for a given configuration finding areas that can be improved to increase concurrency.
Application bottlenecks usually fall into three categories: database, memory leak, or slow algorithm. Finding them involves putting the application in question under stress (i.e. load) for an extended period of time - at least an hour, perhaps up to several days. Jmeter is a good tool for this purpose. One of the things to consider is running the same test with cookie handling enabled (i.e. Jmeter retains cookies and sends with each subsequent request) and disabled - sometimes you get very different results and this is important because the latter is effectively a simulation of what some crawlers do to your site. Details for bottleneck detection follow:
Database
Tables without indices or SQL statements involving multiple joins are frequent app bottlenecks. Every database server I've dealt with, MySQL, SQL Server, and Oracle has some way of logging or identifying slow running SQL statements. MySQL has the slow query log, whereas SQL Server has dynamic management views that track the slowest running SQL. Once you've got your hands on the slow statements use explain plan to see what the database engine is trying to do, use any features that suggest indices, and consider other strategies - such as denormalization - if those two options do not solve the bottleneck.
Memory Leak
Turn on verbose garbage collection logging and a JMX monitoring port. Then use jConsole, which provides much better graphs, to observe trends. In particular leaks usually show up as filling the Old Gen or Perm Gen spaces. Leaks are a bottleneck with the JVM spends increasing amounts of time attempting garbage collection unsuccessfully until an OOM Error is thrown.
Perm Gen implies the need to increase the space as a command line parameter to the JVM. While Old Gen implies a leak where you should stop the load test, generate a heap dump, and then use Eclipse Memory Analysis Tool to identify the leak.
Slow Algorithm
This is more difficult to track down. The most frequent offenders are synchronization, inter process communication (e.g. RMI, web services), and disk I/O. Another common issue is code using nested loops (look mom O(n^2) performance!).
Best way I've found to find these issues absent some deeper knowledge is generating stack traces. These will tell what all threads are doing at a given point in time. What you're looking for are BLOCKED threads or several threads all accessing the same code. This usually points at some slowness within the codebase.