World of Warcraft uses a strictly space-based system.
Oblivion uses a strictly weight-based system.
Baldur's Gate uses a combination of weight and space-based systems.
I've always hated space-based systems because I fill up my inventory with little odds and ends that I could carry a million of in a weight-based system.
I've always hated weight-based systems because the weight you can carry is usually based off of your strength, so weak characters (aka a mage) have to either deal with not being able to carry much or wasting attribute points to raise their strength or some sort of skill point to raise their maximum carry weight.
Mixed systems fill in some of the pros, but you end up with the cons of both. The major thing that it does fix is that weaker characters can fill their bags with all of the smaller items, leaving the stronger character's inventory open for heavy items.
However, during my research I came across The Unbearable Heaviness of Gaming Inventories which is a post by Philippa Warr. It's a great read and she makes valid points. I too fall victim to collecting the rare oddities and such in a game (I've had the Spork in my inventory since I first saw it in Oblivion.)
I do have to agree with reply #7 in that this would remove some of the significance of items. However, the bigger issue is that it removes a major development tactic that extends play time: you would never have to empty your bags. By restricting inventory, at some point (a bajillion times throughout the game) you have to run to town to empty out your bags. As I said, this extends play time and also requires you to pay attention to your inventory and what you're picking up (or just pick everything up and then drudge through the inventory when you run out of space/become over-encumbered.)
This also brings about several other issues: people would just pick up everything that they saw leading to memory issues and the app slowing down or even freezing when trying to open your inventory just to name a couple. So, the solution I've been contemplating involves using the (completely awesome) "sanctuary" idea. At any point in the game you can teleport to your sanctuary where you can deposit items. The space in your sanctuary would be limited to space and your inventory could be limited by either space or weight. You could include the ability to upgrade your sanctuary, thus increasing the space available.
I'm kind of rambling now, but this is just one of the things that's always on my mind and I was wondering what your opinion was on the topic.
- edit -
I forgot to mention this, but obviously there are already several games out there have systems similar to this. Some notable examples are Baldur's Gate 2: The Throne of Bhaal expansion, Fable 3, Diablo 2 (and Diablo 2 style games like Fate and Torchlight.) I mention the Diablo 2 style games because they have town portal (if you have any scrolls) and a chest to store items in every town.