Nowhere in the N.T. do any of the Greek words translated "fellowship" imply fun times. Rather, they talk of:

• The fellowship of the ministering to the saints (II Corinthians 8:4).
• Sacrificial service and financial aid (See for example, I Timothy 6:18).
• The fellowship in the gospel (Philippians 1:5), 
• The defense and confirmation of the gospel, we all are partakers (same word as fellowship) of grace (Philippians 1:7).
• Bringing persecution: We are to emulate Christ's humility and self-sacrificial love (Philippians 2:5-8).
• A fellowship of the Spirit (Phil 2:1).
• Knowing the fellowship of His sufferings, being made conformable unto His death (Philippians 3:10). 
• Communion (i.e. fellowship) of the blood...and body of Christ (I Corinthians 10:16).