Are there any games like Dragon Age and Mass Effect in terms of Class Systems, Character Customization, and Role-Playing?
Well, there is Skyrim. It has the latter two at least, and a class structure only because your character becomes functionally weaker if you try to divide your experience among a ton of different disciplines. Between you and me though, I think Morrowind is much better.
The first two Knights of the Old Republic Games. The first was made by Bioware right before they made Mass Effect, and the second uses the same combat/items/levels systems, so there's a good number of similarities.
Lots. You can look up any western RPG and find a strong element of customization and roleplay. First game I thought of was alpha protocol. It's a very broken game, but at the same time it can be very impressive with the amount of choice and consequence in it. Also you have jade empire that is another game made by bioware. It's a lot like their other games only in china. It also has a very memorable scene where you can openly flirt with the princess and cause everyone around her to faint... Ok it doesn't sound all that fun, but it is.