You are probably already familiar with cpuinfo and meminfo, which tell you about the machine's CPU and memory respectively. You can also get uptime and version information from uptime and version. This, in fact, is where the uname command gets its information.
The net/ directory provides the raw info for various networking information commands, such as route. The text-system communication of /proc goes both ways: As well as accessing information, you can change it by editing the various files. Look at /proc/sys/net/ipv4/ to see some values that you can change if you want.
partitions gives information on the partitions this can be more useful than using df and quicker than fdisk. filesystems lists the filesystems that the kernel can deal with, and marks them with nodev if they're either virtual or networked. This is handy if you're dealing with filesystems on remote hardware, or a Mystery Hard Drive, to check what filesystems you are able to read.
Spend some time having a poke through /proc with the man page to find out what else is there.