It's a lot more than you really need, but Babel does include currencies, in the Locale currency_symbols dictionary. Some may require a little parsing, though; for example, USD is 'US$' rather than just the dollar sign, while others, like the Euro or Yuan, have no such prefix.

I believe Babel uses the CLDR as its source.

You have too many for-loops

for i in course:
    print(i['currency'], i['rate'])

But this need also to search <cube> with attribute currency

course = soup.findAll("cube", currency=True)

course = soup.findAll("cube", {"currenc": True})

or you would have to check if item has attribute currency

for i in course:
    if 'currency' in i.attrs:
        print(i['currency'], i['rate'])

Full code:

import requests
from bs4 import BeautifulSoup

url = 'https://www.ecb.europa.eu/stats/eurofxref/eurofxref-daily.xml?c892a2e0fae19504ef05028330310886'

response = requests.get(url)
soup = BeautifulSoup(response.text, "lxml")

course = soup.find_all("cube", currency=True)

for i in course:
    #print(i)
    print(i['currency'], i['rate'])

Not very elegant or nifty, but you can generate the list once and save to use it later:

import urllib, re
url = "http://www.iso.org/iso/support/faqs/faqs_widely_used_standards/widely_used_standards_other/currency_codes/currency_codes_list-1.htm"
print re.findall(r'\<td valign\="top"\>\s+([A-WYZ][A-Z]{2})\s+\</td\>', urllib.urlopen(url).read())

output:

['AFN', 'EUR', 'ALL', 'DZD', 'USD', 'EUR', 'AOA', 'ARS', 'AMD', 'AWG', 'AUD',
...
'UZS', 'VUV', 'EUR', 'VEF', 'VND', 'USD', 'USD', 'MAD', 'YER', 'ZMK', 'ZWL', 'SDR']

Note that you'll need to prune everything after X.. as they are apparently reserved names, which means that you'll get one rogue entry (SDR, the last element) which you can just delete by yourself.

How about Babel?

from babel import numbers
print numbers.get_currency_symbol('USD', locale='en') # => $1,500.00
print numbers.get_currency_symbol('GBP', locale='fr_FR') # => 1 500,00 £UK

You might not have realised it yet, but all your unimplemented methods will very much look like real_to_dollar:

• ask the user how much of the original currency he wants converted;
• apply a specific conversion rate;
• tell the user the result of the conversion in the desired currency.

So that should be a single function, parametrized by the elements that differ between various calls: name of the origin currency, name of the converted currency, exchange rate.

def convert_currency(from, to, rate):
    user_value = raw_input("How many {}? ".format(from))
    amount = float(user_value)
    conversion = amount * rate
    print " {} {} is equal to {} {}.".format(user_value, from, conversion, to)

Also note the use of format to simplify building a string with numbers.

You would then call it convert_currency("reais", "dollars", 0.26) or convert_currency(" dollars", "reias", 3.85).

However, having to use a bunch of ifs to know what parameters to use (like you would have used a bunch of ifs to know which function to call) is not that great and can be a burden to maintain and expand. You could use a second dictionary to map couples of currencies to exchange rates:

RATES = {
    ("BRL", "USD"): 0.26,
    ("USD", "BRL"): 3.85,
    # Expand as necessary
}

And just have to get the rate using RATES[(user_choice1, user_choice2)].

Code Style Improvements

• "Flat is better than nested". You can make an early exit in case of invalid input:

  import sys
  
  try:
      amount = float(input("Enter amount: "))
  except ValueError:
      print("Invalid input. Please enter only numbers.")
      sys.exit(1)
  

  That will allow you to remove the else: part and continue on the top-level. Or, you can let the user retry the input until it is valid

• on the same topic of decreasing nestedness depth - add more early exists. For instance, if input currencies are invalid, throw an error and exit. Then, remove the else: and continue with your "positive case" logic on the same level. This should improve overall readability
• define the constants, like the list of currencies, as per PEP8 - in upper case (reference)
• put the main execution logic to under if __name__ == '__main__':
• you can simplify if output_cur != '': with just if output_cur:
• I'm not sure why you are importing datetime from _datetime (with underscore). I would expect the import to be from datetime import datetime
• don't put comment for obvious parts of the code. For example, "importing required libraries" does not provide any useful information.

• organize imports per PEP8 - stdlib libraries, then a newline, third-parties, a new line and then your "local" dependencies, all sorted alphabetically:

  from datetime import datetime
  
  from babel import numbers
  import pycountry
  import requests
  

Other High-level ideas

• define custom exceptions. Instead of using the error_sev and error_inp functions where you print errors, define custom exceptions like InvalidCountryValueError. Throw it with your custom message inside
• since you are posting it on github, consider organizing the project properly - add requirements.txt with the list of dependencies, add more documentation, tests - see more at Open Sourcing a Python Project the Right Way
• on the related topic: currently, there is only one way to use your program. Consider someone who wants to use your library as an API - not going through the standard in inputs, but calling a function asking for currency rates. Thinking about your program this way may help you to re-design it a bit, apply "Extract Method" and other refactoring methods. Also, if you would try to add tests, you will quickly realize that there is no easy way to unittest the program - usually a red flag when designing clean and modular APIs

Performance notes

• I'd use a set to keep the supported list of currencies. Since you check the input currencies to be valid with in, this should have a positive impact on performance:

  CURRENCIES = {
      'USD', 'JPY', 'BGN', 'CZK', 'DKK', 'GBP', 'HUF', 'PLN', 'RON', 'SEK', 'CHF', 'NOK', 'HRK', 'RUB', 'TRY',
      'AUD', 'BRL', 'CAD', 'CNY', 'HKD', 'IDR', 'ILS', 'INR', 'KRW', 'MXN', 'MYR', 'NZD', 'PHP', 'SGD', 'THB',
      'ZAR', 'ISK'
  }