So, yea The Sims 2. Launched, was great. Don't run so good now on everything. Here's various links and files to help that. All links are current and working at the time of writing. Let me know if something breaks. All mods were tested on the Ultimate Collection available through Origin, though they should be compatible with all EPs up to Apartment Life. Consult each page for details.
Cyjon's Variuous Fixes
Cyjon's Sims 2 Mods 'n' Stuff get a sort of special mention. Cyjon has a lot of fixes and tweaks, though I highly recommend that you wait and see what issues you have before you install mods all willy-nilly.
Many of these are from Nopoke at MTS which, yes, requires an account. However, the account is free and you're probably gonna need one anyway sooner or later.
The description from the download page follows. This mod fixes the serving plate with crepes suzette. By default it looks empty when there's one crepe on it, and a crepe shows up on it when it's actually empty. Now, it looks empty if it's empty, and a crepe shows up if there's a crepe on it.
I use these, I like these, I recommend these. However, these things are not broken in the same sense, exactly. Rather they change (what we assume was) deliberate behavior on the part of the devlopers.
This is actually two things, but both are reccomended. The SCRIPTORIUM makes it easier to install things like modular stairs and custom walls. Gunmod's Radiance Light System improves how the game handles lighting and fixes many of the EA/Maxis lights at the same time.
Some Additional Stuff
Mostly graphical things to improve the experience of your eyeballs and some CC to get you started.
Hosted here because the original links are all dead (as far as I know). Some nice Maxis-match skintones that actually improve how sims look, particularly with Gunmod's Radiance Light System installed-- However, that is not required. These are replacements. Also, they do have nipples on both them male and feamle sims but you need other things to really see them properly so they are still safely PG-13.