If you are looking for a way to look up the ingredients in your skin care products, this may be a good place to start.  These are a few resources that I use to look up cosmetic ingredients as I like to be able to recognize the what each ingredient is and it's purpose.  

What's in your skin care products?

For instance, you go grocery shopping and look at the ingredients for ice cream: milk, cream, eggs - sounds good!  Why not do the same for cosmetics?  After all, you are going to put it all up on your face, right?  Once you recognize the most commonly used ingredients you will be able to say "Oh, this is a preservative" or "Oh, this has Vitamin C in it." You can even take it a step further:  When faced with two similarly priced products, you can compare the ingredients and make a more informed purchasing decision based on your skin's needs.

DHC Skincare & Ingredients Glossary

I am adding this one above Paula's Choice because of how user friendly it is.  All of the ingredients are on one page so it is easier to look up ingredients while shopping around.  It does not contain the research or sources that the other ingredient databases have, but it gives you exactly what you need when you are searching for something quickly.

Paula's Choice Cosmetic Ingredient Dictionary

This is my go-to database when I am shopping around and come across an ingredient I don't recognize.  You will find most ingredients you are inquiring about here so it is kind of a one stop shop for information.  I also appreciate how sources are cited for many of the ingredients listed so you can use it as a springboard for further research.

COSDNA

I don't use this site often, but I really should.  You can search by the ingredient or by the product and it's cool because say you want to buy something with Green Tea Extract in it - you can search by the ingredient and it will list products that contain Green Tea Extract.  When you search by product you are taken to a breakdown of ingredients in the product where they are ranked for:  Acne, Irritant and Safety.  If you are very acne prone, you can check to see if a product you are considering contains common acne triggers.  This database contains a lot of user submitted information so it is constantly growing.

EWG's Skin Deep Cosmetic Database

This database does not go into much detail about what the particular ingredient is used for like Paula's Choice, but it does provide a list of the basic functions of the ingredient as well as alternate names that the ingredient may go by.  It also brings to light any concerns that may be associated with the ingredient and lists sources.

Examine.com - Your Unbiased Source on Nutrition and Supplements

This database does not have an extensive list of cosmetic ingredients, but the ones they do have are easy to understand.  They even take things a step further and summarize various scientific studies and provide sources as well.  The database is more for nutrition / supplement ingredient information rather than cosmetic information.

National Center for Biotechnology Information

This is one of my favorite sites to go to if you enjoy reading research material.  Since I like to DIY serums, I come here to read about the effectiveness of certain ingredients such as L-Ascorbic Acid and Niacinamide.  I like to learn how the experiments were performed and what the results were.

In the end, if you just want a quick go-to database where you will find a majority of the ingredients you are looking for; I would recommend checking DHC Skincare & Ingredients Glossary or Paula's Choice Cosmetic Ingredient Dictionary first; then check the product out on COSDNA for acne triggers / irritants if that is an issue for you.  I will continue to update this post if I come across any other databases that I have found to be useful.