Governor Limit question: Large data set. How do I avoid hitting governor limits?
When dealing with large data sets your best bet is to leverage batch apex. This has the limitation of being asynchronous, but you can process way more data than you're able to normally. It's simpler than getting bogged down with @future based calls (an older technology on the platform) and is the only way to get a larger set of governor limits to work with.
The trigger could create an instance of your batch class, passing to it (via the constructor or similar) the list of IDs for the records to be processed.
I would look at using Batch Apex. It can handle the large data sets. I have found that the code is generally cleaner to write than triggers (e.g., different logic for insert/update, etc.) when the data model is very complex.
Even if your list size is greater than 200, Salesforce will break up your lists into chunks of 200 for trigger processing. Each chunk contributes to the same shared limit, though. If you were to perform one bulkified SOQL query in a single trigger you'd be able to process 100 * 200 = 20,000 records of that object in a single transaction until you hit the 101 max. If you are just using DML you'd have 150 * 200 = 30,000. That only accounts for a situation where a single query or single dml statement is issued.
In a complex data model you can definitely have many more queries occuring in your triggers, because your single save will trigger saves on other related records (e.g., roll-up summary triggering save in parent). It is worth keeping in mind what happens when you save a record when you design. If you design your solution to have triggers on every object it can be cumbersome to figure out why something is getting updated on a related record and can be harder to maintain.
On top of all of that, if your data model is really that complex you have to consider what will happen when you set up unit tests. If you have triggers on every object with many queries and updates you can definitely get into a situation where you approach the 101 SOQL Query limit when you are setting up the unit test data.
There's a developer force blog post that has a some high level summaries on working with large data sets and links to other resources.
We do something similar and process tens of thousands of records every day as part of our "end of day" process. You have several tools in your toolbox. Batch Apex is already mentioned in the answers. The other three tools you can use are @future jobs, queueable jobs, and scheduled jobs. If you don't need to run all the processes synchronously, these three will help you in increasing the limit by breaking down the process into multiple independent processes with their own governor limits. Queueable Jobs are newly introduced and are very powerful and flexible.