Tes4Mod:Stabilization and Optimization

First and foremost, do not underestimate the load that modified Oblivion can put on your machine...

Stabilization
...go away crashes

Some Tips

Install the unofficial official patches.
Apply helpful tweaks to your Oblivion.ini and other INI files.
Cycle through a set of saves instead of saving regularly on top of the same file.
Read the ReadMes for mods before installing them, especially to find out about compatibility issues.
Making sure your load order is correct can fix many issues.
Keep mods up to date.
Do not install a bunch of mods at once.
Keep your system specs in mind when downloading visual enhancements and mods that add NPCs and creatures.
Always be on the lookout for compatibility patches.
Clean your plugin list.
Always rebuild the bashed patch after making load order changes.
Eliminate unnecessary background processes (i.e., firewall, anti-virus.)
If upgrading, focus on the CPU, as most current GPUs are more than adequate for Oblivion.
A sound card with support for hardware acceleration is a cheap investment with a huge return.
Defrag your hard drive periodically, especially after installing big applications.
When updating or switching to different (closely-related) versions of a mod, do a clean update.

Optimization
...getting a few extra fps and taking a little more pressure off of your CPU

Optimization, here, is all about getting more out of your current setup. The only change you will see to your game after following these recommendations is higher FPS and less pressure on your system. There are replacers, plugins and modules to help do this, and this will give you an introduction to them all.

Tips

Be careful tweaking INI settings and overclocking.
Turn off unnecessary services before playing.
Disable services through msconfig.
Turn off your antivirus, firewall, etc.
You can use programs such as Game Booster to facilitate this process. (See Programs & Utilities.)
Invest in a sound card with hardware acceleration.
The separate card would take much of the load for sound processing off the CPU.
It is one of the cheaper computer upgrades, but the return is significant.
PyFFI-Optimize meshes for large files, including the original Oblivion meshes.
Some mods have PyFFI-optimized mesh patches uploaded at TESNexus, and a number of mods are already PyFFI-optimized.
If you are willing, running the game at a lower resolution can offer a considerable performance increase.
Less NPCs and creatures, means less processing work for the CPU.
Repacking BSAs with no compression level will allow the game to access the files quicker.
Packing loose files into BSAs will improve performance and, coupled with the tip above, offer an even greater boost.

See Also
Basic Plugin Cleaning
BSA Repacking
Mod Settings Configuration
Oblivion.ini Tweaks
Popular Outdated Mods
Python File Format Interface
Stabilization and Optimization Mods

External Links
Oldblivion - if you are using an older machine...
The Oblivion Performance Project - a.k.a. "TOPP"
UOP List of Fixes - Baldurdash
 Guide   How to Smooth PC Oblivion FPS] - BethSoft Mods Forum <-- Author: Albertine (Some of the tweaks are pretty advanced and require testing. Be careful.)