This hotel room is damp, dirty, and smells of stale urine and I still can't afford it.

Hotel rooms are just not in my budget and I am guessing that if you're here, on my blog now, it probably isn't in yours either. Do not let this stop you from traveling! There are some cheap, even free alternatives!  Backpacking Hostels

Santiago de Compostela, Spain. Backpacking hostel I worked for in 2012.
Hostels get a bad rep. If you have ever seen the horror movie Hostel you probably want nothing to do with one (severed limbs, no thank you!) but please remember it is just a movie folks. Hostels are actually a fairly ordinary thing in Europe and in many cases, just seem strange and foreign to us Americans. I like to think of it as having a sleep over with a potential friend!  If bringing a towel is an inconvenience you can rent one for a few dollars! HostelWorld is a very well known/popular hostel finder worldwide. Use it too!

Airbnb

San Lorenzo, Italy $67/night 2ppl
If you aren't comfortable sleeping with 4+ others in a single room and can't afford the outrageous prices hostels charge for individual rooms then Airbnb is perfect. You pay for a room in someones home. A private room for less than what it costs to sleep next to several others in a hostel? I'LL TAKE IT!
Couchsurfing

Don't want to pay for a room at all? Sleep on someone's couch (or bed!) This is a groovy travel platform that connects you to other travelers who have a couch to lend! You might even get lucky and sleep in a bed! Stick with people who have good references. But whatever you do, be respectful and don't treat it as you would a hotel room. Create relationships with your hosts, not sleep and leave. 

University Dorms

Trinity College. Dublin, Ireland. Twin ensuite accomodation. While students are away for the summer some universities rent out dorm rooms to travelers at a low cost. Isn't that innovative? Here is a link that will guide you in the right direction for college dorms! I must make a confession: After working at several backpacking hostels, a dirty and damp hotel room doesn't sound half bad if it means privacy!

Cheapo Transportation

The plane ticket over to Europe has to be one of the  most expensive things about my whole travel itinerary.  In 2012, I flew from Phoenix, AZ, USA to Dublin, Ireland  for around $804 USD in September. This year I will be flying from Phoenix, AZ, USA to Dublin, Ireland  for around $944 USD in June.  If I really looked hard enough I could find better deals but these are STILL going to look incredibly cheap next to the price of the same flight from websites like Expedia and Travelocity. 

What do I use?  Hipmunk You won't find cheaper airfare then on Hipmunk. I've compared Hipmunk to other airfare listers such as Expedia and Travelocity, Hipmunk has always been the cheapest.
How can I find the cheapest days to purchase my ticket?  Matrix Airfare Search It is what the travel agents use.   
Other important tips:  - Fly out midweek (cheaper than flying Friday when everyone else wants to) - Buy tickets on Tuesday (when new deals are released) - Allow your dates to be flexible (it could be $1200 on the 25th but $850 the 27th)

Cheap budget airlines: 

Ryanair (Europe)
Easyjet (Europe)
Allegiant Air (USA)  Have a cheap flight from Phoenix to Honolulu, Hawaii for around $300 round-trip (even next day)

Ryanair the Ikea of Airlines? Spain 2012

ALSO one of my favorite websites for traveling cheaply excluding flights is Seat 61 *Highly recommend*